Future value of $1,000 after 5 years at 10% annual interest rate. Introduction: Time Value of Money : It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Question

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Answer 1

Question

Chapter 5, Problem 41SP

a.

Summary Introduction

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

a.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 1

Table (1)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,610.50.

Conclusion

Future value of $1,000 is $1,610.51.

b.

Summary Introduction

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

b.

Expert Solution

Explanation of Solution

Calculation spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 2

Table (2)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in required field.

Conclusion

Investment future values are different for the different years with 0%, 5% and 20% interest rate.

c.

Summary Introduction

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

c.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 3

Table (3)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $620.92.

Conclusion

Present value of $1,000 is $620.92 at 10 % discount rate.

d.

Summary Introduction

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

d.

Expert Solution

Explanation of Solution

Calculationin spreadsheet by “RATE” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 4

Table (4)

Steps required to calculate present value by using “RATE” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “RATE” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 14.87%

Conclusion

The rate of return is14.87%.

e.

Summary Introduction

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2%

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

e.

Expert Solution

Explanation of Solution

Calculation is solved in spreadsheet by “NPER” formula

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 5

Table (5)

Steps required to calculate present value by using “NPER” function in excel are given,

Select ‘Formulas’ option from Menu Bar of excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPER” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 35 years.

Conclusion

Conclusion:

It will take 35 years to double the population from 36.5 million to 73 million.

f.

Summary Introduction

To calculate: Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

f.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 6

Table (6)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,352.16.

So, the present value is $3,352.16.

Calculation of future value of annuity in spreadsheet by using “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 7

Table (7)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $6,742.38.

So the future value is $6,742.38.

Conclusion

Present value is $3,352.16 and future value is $6,742.38 of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

g.

Summary Introduction

To calculate: Present and future value of part ‘f’ if the annuity is due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

g.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 8

Table (8)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,351.66.

Present value of annuity due is $3,351.66.

Future value of annuity in spreadsheet by “FV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 9

Table (9)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $7,753.74

Future value of annuity due is $7,753.74.

Conclusion

Present value of annuity due is $3,351.66 while future value is $7,753.74.

h.

Summary Introduction

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

h.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 10

Table (10)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $613.91.

Present value is $613.91.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 11

Table (11)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Future value of annuity is $1,628.89.

Conclusion

Present andfuture value for $1,000, due in 5 years with 10% semiannual compoundingwill be $613.91 and $1,628.89, respectively.

i.

Summary Introduction

To calculate: Annual payments for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

i.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 12

Table (12)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity is $149.03.

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 13

Table (13)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity due is $137.99.

Conclusion

Annual payments are$149.03 for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due is $137.99.

j.

Summary Introduction

To calculate: Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

j.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “NPV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 14

Table (14)

Steps required to calculate present value by using “NPV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $581.59.

Present value is $581.59.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 15

Table (15)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $732.54.

Future value is $732.54.

Conclusion

Present value is $581.89 while future value is $732.54.

k.1.

Summary Introduction

To calculate: Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

k.1.

Expert Solution

Explanation of Solution

Given for Bank A,

Nominal interest rate is 5%.

Compounding is annual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 1 for M.

(EFF%)=(1+0.051)1−1.0=0.05=5%

So, effective annual rate for Bank A is 5%.

Given for Bank B,

Nominal interest rate is 5%.

Compounding is semiannual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 2 for M.

(EFF%)=(1+0.052)2−1.0=0.0506=5.06%

So,effective annual rate for Bank B is 5.06%.

Given for Bank C,

Nominal interest rate is 5%.

Compounding is quarterly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 4 for M.

(EFF%)=(1+0.054)4−1.0=0.0509=5.09%

So, effective annual rate for Bank C is 5.09%.

Given for Bank D,

Nominal interest rate is 5%.

Compounding ismonthly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 12 for M.

(EFF%)=(1+0.0512)12−1.0=0.0511=5.11%

So, effective annual rate for Bank D is 5.11%.

Given for Bank E,

Nominal interest rate is 5%.

Compounding is daily.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 365 for M.

(EFF%)=(1+0.05365)365−1.0=0.0512=5.12%

So, effective annual rate for Bank E is 5.12%.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 16

Table (16)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 250, $5,253,$5,254.50, $5,255.50 and $5,256.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 17

Table (17)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 512, $5,518.80, $5,521.95, $5,524.06 and $5,525.11.

Conclusion

Each bank pays different effective rate as there compounding is different, the rates are5% for bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E, also the future values also change on the basis of their number of periods.

2.

Summary Introduction

To explain: If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

2.

Expert Solution

Answer to Problem 41SP

No, it is not possible for the banks to equally attract funds.

The nominal rate which causes same effective rate for all banks are,

Particulars	A	B	C	D	E
Nominalrate	5%	5.06%	5.09%	5.11%	5.12%

Table (18)

Explanation of Solution

Bank will not be equally able to attract funds because of compounding, as people prefer to invest in that bank which have more frequent compounding in comparison to the bank which have lesser frequent compounding.
Nominal rate is opposite of the effective rate which is calculated in part ‘1’. The nominal rate indicated in above table will cause same effective rate for all banks as it is for A bank.

Conclusion

Due to frequent compounding, banks will not be able to equally attract funds and the nominal rate will be 5% for Bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E.

3.

Summary Introduction

To calculate: Present value of amount to get $5,000 after 1 year.

3.

Expert Solution

Explanation of Solution

Calculation of payment to be made in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 18

Table (19)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

So, the amounts to be paid are$4,761.90,$2498.10,$1,102.40,$296.96 and $15.83.

4.

Summary Introduction

To explain: If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

4.

Expert Solution

Answer to Problem 41SP

Yes, a rational investor would be indifferent between the banks.

Explanation of Solution

Rational investor chooses the bank which will provide him better return so he would be indifferent, if all the banks are giving same effective rate because he chooses the bank which will have more frequent compounding than others.

Conclusion

A bank offers frequent compounding is able to attract more number of customers than others.

Summary Introduction

To prepare: Amortization schedule to show annual payments, interest payments, principal payments, and beginning and ending loan balances.

Amortization:

Amotization means to write off or pay the debt over the priod of time it can be for loan or intangible assets. Its main purpose is to get cost recovery. Example of amortization is ,an automobile company that spent $20 million dollars on a design patent with a useful life of 20 years. The amortization value for that company will be $1 million each year.

Expert Solution

Explanation of Solution

Calculation of annual installment is done by using “PMT” formula in spreadsheet at the amortization schedule.

Amortization schedule is prepared below,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 19

Table (20)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

Amortization schedule represents annual payments, interest payments, principal payments, and beginning and ending loan balances.

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Consider the following simplified financial statements for the Yoo Corporation (assuming no income taxes): Income Statement Balance Sheet Sales Costs $ 40,000 Assets 34,160 $26,000 Debt Equity $ 7,000 19,000 Net income $ 5,840 Total $26,000 Total $26,000 The company has predicted a sales increase of 20 percent. Assume Yoo pays out half of net income in the form of a cash dividend. Costs and assets vary with sales, but debt and equity do not. Prepare the pro forma statements. (Input all amounts as positive values. Do not round intermediate calculations and round your answers to the nearest whole dollar amount.) Pro forma income statement Sales Costs $ 48000 40992 Assets $ 31200 Pro forma balance sheet Debt 7000 Equity 19000 Net income $ 7008 Total $ 31200 Total 30304 What is the external financing needed? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign.) External financing needed $ 896

Answer 2

Question

Chapter 5, Problem 41SP

a.

Summary Introduction

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

a.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 1

Table (1)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,610.50.

Conclusion

Future value of $1,000 is $1,610.51.

b.

Summary Introduction

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

b.

Expert Solution

Explanation of Solution

Calculation spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 2

Table (2)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in required field.

Conclusion

Investment future values are different for the different years with 0%, 5% and 20% interest rate.

c.

Summary Introduction

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

c.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 3

Table (3)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $620.92.

Conclusion

Present value of $1,000 is $620.92 at 10 % discount rate.

d.

Summary Introduction

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

d.

Expert Solution

Explanation of Solution

Calculationin spreadsheet by “RATE” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 4

Table (4)

Steps required to calculate present value by using “RATE” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “RATE” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 14.87%

Conclusion

The rate of return is14.87%.

e.

Summary Introduction

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2%

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

e.

Expert Solution

Explanation of Solution

Calculation is solved in spreadsheet by “NPER” formula

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 5

Table (5)

Steps required to calculate present value by using “NPER” function in excel are given,

Select ‘Formulas’ option from Menu Bar of excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPER” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 35 years.

Conclusion

Conclusion:

It will take 35 years to double the population from 36.5 million to 73 million.

f.

Summary Introduction

To calculate: Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

f.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 6

Table (6)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,352.16.

So, the present value is $3,352.16.

Calculation of future value of annuity in spreadsheet by using “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 7

Table (7)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $6,742.38.

So the future value is $6,742.38.

Conclusion

Present value is $3,352.16 and future value is $6,742.38 of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

g.

Summary Introduction

To calculate: Present and future value of part ‘f’ if the annuity is due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

g.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 8

Table (8)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,351.66.

Present value of annuity due is $3,351.66.

Future value of annuity in spreadsheet by “FV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 9

Table (9)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $7,753.74

Future value of annuity due is $7,753.74.

Conclusion

Present value of annuity due is $3,351.66 while future value is $7,753.74.

h.

Summary Introduction

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

h.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 10

Table (10)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $613.91.

Present value is $613.91.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 11

Table (11)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Future value of annuity is $1,628.89.

Conclusion

Present andfuture value for $1,000, due in 5 years with 10% semiannual compoundingwill be $613.91 and $1,628.89, respectively.

i.

Summary Introduction

To calculate: Annual payments for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

i.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 12

Table (12)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity is $149.03.

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 13

Table (13)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity due is $137.99.

Conclusion

Annual payments are$149.03 for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due is $137.99.

j.

Summary Introduction

To calculate: Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

j.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “NPV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 14

Table (14)

Steps required to calculate present value by using “NPV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $581.59.

Present value is $581.59.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 15

Table (15)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $732.54.

Future value is $732.54.

Conclusion

Present value is $581.89 while future value is $732.54.

k.1.

Summary Introduction

To calculate: Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

k.1.

Expert Solution

Explanation of Solution

Given for Bank A,

Nominal interest rate is 5%.

Compounding is annual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 1 for M.

(EFF%)=(1+0.051)1−1.0=0.05=5%

So, effective annual rate for Bank A is 5%.

Given for Bank B,

Nominal interest rate is 5%.

Compounding is semiannual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 2 for M.

(EFF%)=(1+0.052)2−1.0=0.0506=5.06%

So,effective annual rate for Bank B is 5.06%.

Given for Bank C,

Nominal interest rate is 5%.

Compounding is quarterly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 4 for M.

(EFF%)=(1+0.054)4−1.0=0.0509=5.09%

So, effective annual rate for Bank C is 5.09%.

Given for Bank D,

Nominal interest rate is 5%.

Compounding ismonthly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 12 for M.

(EFF%)=(1+0.0512)12−1.0=0.0511=5.11%

So, effective annual rate for Bank D is 5.11%.

Given for Bank E,

Nominal interest rate is 5%.

Compounding is daily.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 365 for M.

(EFF%)=(1+0.05365)365−1.0=0.0512=5.12%

So, effective annual rate for Bank E is 5.12%.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 16

Table (16)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 250, $5,253,$5,254.50, $5,255.50 and $5,256.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 17

Table (17)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 512, $5,518.80, $5,521.95, $5,524.06 and $5,525.11.

Conclusion

Each bank pays different effective rate as there compounding is different, the rates are5% for bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E, also the future values also change on the basis of their number of periods.

2.

Summary Introduction

To explain: If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

2.

Expert Solution

Answer to Problem 41SP

No, it is not possible for the banks to equally attract funds.

The nominal rate which causes same effective rate for all banks are,

Particulars	A	B	C	D	E
Nominalrate	5%	5.06%	5.09%	5.11%	5.12%

Table (18)

Explanation of Solution

Bank will not be equally able to attract funds because of compounding, as people prefer to invest in that bank which have more frequent compounding in comparison to the bank which have lesser frequent compounding.
Nominal rate is opposite of the effective rate which is calculated in part ‘1’. The nominal rate indicated in above table will cause same effective rate for all banks as it is for A bank.

Conclusion

Due to frequent compounding, banks will not be able to equally attract funds and the nominal rate will be 5% for Bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E.

3.

Summary Introduction

To calculate: Present value of amount to get $5,000 after 1 year.

3.

Expert Solution

Explanation of Solution

Calculation of payment to be made in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 18

Table (19)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

So, the amounts to be paid are$4,761.90,$2498.10,$1,102.40,$296.96 and $15.83.

4.

Summary Introduction

To explain: If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

4.

Expert Solution

Answer to Problem 41SP

Yes, a rational investor would be indifferent between the banks.

Explanation of Solution

Rational investor chooses the bank which will provide him better return so he would be indifferent, if all the banks are giving same effective rate because he chooses the bank which will have more frequent compounding than others.

Conclusion

A bank offers frequent compounding is able to attract more number of customers than others.

Summary Introduction

To prepare: Amortization schedule to show annual payments, interest payments, principal payments, and beginning and ending loan balances.

Amortization:

Amotization means to write off or pay the debt over the priod of time it can be for loan or intangible assets. Its main purpose is to get cost recovery. Example of amortization is ,an automobile company that spent $20 million dollars on a design patent with a useful life of 20 years. The amortization value for that company will be $1 million each year.

Expert Solution

Explanation of Solution

Calculation of annual installment is done by using “PMT” formula in spreadsheet at the amortization schedule.

Amortization schedule is prepared below,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 19

Table (20)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

Amortization schedule represents annual payments, interest payments, principal payments, and beginning and ending loan balances.

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Answer 3

Question

Chapter 5, Problem 41SP

a.

Summary Introduction

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

a.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 1

Table (1)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,610.50.

Conclusion

Future value of $1,000 is $1,610.51.

b.

Summary Introduction

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

b.

Expert Solution

Explanation of Solution

Calculation spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 2

Table (2)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in required field.

Conclusion

Investment future values are different for the different years with 0%, 5% and 20% interest rate.

c.

Summary Introduction

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

c.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 3

Table (3)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $620.92.

Conclusion

Present value of $1,000 is $620.92 at 10 % discount rate.

d.

Summary Introduction

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

d.

Expert Solution

Explanation of Solution

Calculationin spreadsheet by “RATE” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 4

Table (4)

Steps required to calculate present value by using “RATE” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “RATE” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 14.87%

Conclusion

The rate of return is14.87%.

e.

Summary Introduction

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2%

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

e.

Expert Solution

Explanation of Solution

Calculation is solved in spreadsheet by “NPER” formula

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 5

Table (5)

Steps required to calculate present value by using “NPER” function in excel are given,

Select ‘Formulas’ option from Menu Bar of excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPER” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 35 years.

Conclusion

Conclusion:

It will take 35 years to double the population from 36.5 million to 73 million.

f.

Summary Introduction

To calculate: Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

f.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 6

Table (6)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,352.16.

So, the present value is $3,352.16.

Calculation of future value of annuity in spreadsheet by using “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 7

Table (7)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $6,742.38.

So the future value is $6,742.38.

Conclusion

Present value is $3,352.16 and future value is $6,742.38 of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

g.

Summary Introduction

To calculate: Present and future value of part ‘f’ if the annuity is due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

g.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 8

Table (8)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,351.66.

Present value of annuity due is $3,351.66.

Future value of annuity in spreadsheet by “FV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 9

Table (9)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $7,753.74

Future value of annuity due is $7,753.74.

Conclusion

Present value of annuity due is $3,351.66 while future value is $7,753.74.

h.

Summary Introduction

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

h.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 10

Table (10)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $613.91.

Present value is $613.91.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 11

Table (11)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Future value of annuity is $1,628.89.

Conclusion

Present andfuture value for $1,000, due in 5 years with 10% semiannual compoundingwill be $613.91 and $1,628.89, respectively.

i.

Summary Introduction

To calculate: Annual payments for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

i.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 12

Table (12)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity is $149.03.

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 13

Table (13)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity due is $137.99.

Conclusion

Annual payments are$149.03 for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due is $137.99.

j.

Summary Introduction

To calculate: Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

j.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “NPV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 14

Table (14)

Steps required to calculate present value by using “NPV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $581.59.

Present value is $581.59.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 15

Table (15)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $732.54.

Future value is $732.54.

Conclusion

Present value is $581.89 while future value is $732.54.

k.1.

Summary Introduction

To calculate: Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

k.1.

Expert Solution

Explanation of Solution

Given for Bank A,

Nominal interest rate is 5%.

Compounding is annual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 1 for M.

(EFF%)=(1+0.051)1−1.0=0.05=5%

So, effective annual rate for Bank A is 5%.

Given for Bank B,

Nominal interest rate is 5%.

Compounding is semiannual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 2 for M.

(EFF%)=(1+0.052)2−1.0=0.0506=5.06%

So,effective annual rate for Bank B is 5.06%.

Given for Bank C,

Nominal interest rate is 5%.

Compounding is quarterly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 4 for M.

(EFF%)=(1+0.054)4−1.0=0.0509=5.09%

So, effective annual rate for Bank C is 5.09%.

Given for Bank D,

Nominal interest rate is 5%.

Compounding ismonthly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 12 for M.

(EFF%)=(1+0.0512)12−1.0=0.0511=5.11%

So, effective annual rate for Bank D is 5.11%.

Given for Bank E,

Nominal interest rate is 5%.

Compounding is daily.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 365 for M.

(EFF%)=(1+0.05365)365−1.0=0.0512=5.12%

So, effective annual rate for Bank E is 5.12%.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 16

Table (16)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 250, $5,253,$5,254.50, $5,255.50 and $5,256.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 17

Table (17)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 512, $5,518.80, $5,521.95, $5,524.06 and $5,525.11.

Conclusion

Each bank pays different effective rate as there compounding is different, the rates are5% for bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E, also the future values also change on the basis of their number of periods.

2.

Summary Introduction

To explain: If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

2.

Expert Solution

Answer to Problem 41SP

No, it is not possible for the banks to equally attract funds.

The nominal rate which causes same effective rate for all banks are,

Particulars	A	B	C	D	E
Nominalrate	5%	5.06%	5.09%	5.11%	5.12%

Table (18)

Explanation of Solution

Bank will not be equally able to attract funds because of compounding, as people prefer to invest in that bank which have more frequent compounding in comparison to the bank which have lesser frequent compounding.
Nominal rate is opposite of the effective rate which is calculated in part ‘1’. The nominal rate indicated in above table will cause same effective rate for all banks as it is for A bank.

Conclusion

Due to frequent compounding, banks will not be able to equally attract funds and the nominal rate will be 5% for Bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E.

3.

Summary Introduction

To calculate: Present value of amount to get $5,000 after 1 year.

3.

Expert Solution

Explanation of Solution

Calculation of payment to be made in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 18

Table (19)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

So, the amounts to be paid are$4,761.90,$2498.10,$1,102.40,$296.96 and $15.83.

4.

Summary Introduction

To explain: If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

4.

Expert Solution

Answer to Problem 41SP

Yes, a rational investor would be indifferent between the banks.

Explanation of Solution

Rational investor chooses the bank which will provide him better return so he would be indifferent, if all the banks are giving same effective rate because he chooses the bank which will have more frequent compounding than others.

Conclusion

A bank offers frequent compounding is able to attract more number of customers than others.

Summary Introduction

To prepare: Amortization schedule to show annual payments, interest payments, principal payments, and beginning and ending loan balances.

Amortization:

Amotization means to write off or pay the debt over the priod of time it can be for loan or intangible assets. Its main purpose is to get cost recovery. Example of amortization is ,an automobile company that spent $20 million dollars on a design patent with a useful life of 20 years. The amortization value for that company will be $1 million each year.

Expert Solution

Explanation of Solution

Calculation of annual installment is done by using “PMT” formula in spreadsheet at the amortization schedule.

Amortization schedule is prepared below,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 19

Table (20)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

Amortization schedule represents annual payments, interest payments, principal payments, and beginning and ending loan balances.

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Answer 4

Question

Chapter 5, Problem 41SP

a.

Summary Introduction

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

a.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 1

Table (1)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,610.50.

Conclusion

Future value of $1,000 is $1,610.51.

b.

Summary Introduction

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

b.

Expert Solution

Explanation of Solution

Calculation spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 2

Table (2)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in required field.

Conclusion

Investment future values are different for the different years with 0%, 5% and 20% interest rate.

c.

Summary Introduction

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

c.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 3

Table (3)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $620.92.

Conclusion

Present value of $1,000 is $620.92 at 10 % discount rate.

d.

Summary Introduction

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

d.

Expert Solution

Explanation of Solution

Calculationin spreadsheet by “RATE” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 4

Table (4)

Steps required to calculate present value by using “RATE” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “RATE” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 14.87%

Conclusion

The rate of return is14.87%.

e.

Summary Introduction

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2%

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

e.

Expert Solution

Explanation of Solution

Calculation is solved in spreadsheet by “NPER” formula

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 5

Table (5)

Steps required to calculate present value by using “NPER” function in excel are given,

Select ‘Formulas’ option from Menu Bar of excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPER” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 35 years.

Conclusion

Conclusion:

It will take 35 years to double the population from 36.5 million to 73 million.

f.

Summary Introduction

To calculate: Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

f.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 6

Table (6)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,352.16.

So, the present value is $3,352.16.

Calculation of future value of annuity in spreadsheet by using “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 7

Table (7)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $6,742.38.

So the future value is $6,742.38.

Conclusion

Present value is $3,352.16 and future value is $6,742.38 of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

g.

Summary Introduction

To calculate: Present and future value of part ‘f’ if the annuity is due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

g.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 8

Table (8)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,351.66.

Present value of annuity due is $3,351.66.

Future value of annuity in spreadsheet by “FV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 9

Table (9)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $7,753.74

Future value of annuity due is $7,753.74.

Conclusion

Present value of annuity due is $3,351.66 while future value is $7,753.74.

h.

Summary Introduction

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

h.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 10

Table (10)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $613.91.

Present value is $613.91.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 11

Table (11)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Future value of annuity is $1,628.89.

Conclusion

Present andfuture value for $1,000, due in 5 years with 10% semiannual compoundingwill be $613.91 and $1,628.89, respectively.

i.

Summary Introduction

To calculate: Annual payments for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

i.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 12

Table (12)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity is $149.03.

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 13

Table (13)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity due is $137.99.

Conclusion

Annual payments are$149.03 for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due is $137.99.

j.

Summary Introduction

To calculate: Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

j.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “NPV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 14

Table (14)

Steps required to calculate present value by using “NPV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $581.59.

Present value is $581.59.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 15

Table (15)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $732.54.

Future value is $732.54.

Conclusion

Present value is $581.89 while future value is $732.54.

k.1.

Summary Introduction

To calculate: Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

k.1.

Expert Solution

Explanation of Solution

Given for Bank A,

Nominal interest rate is 5%.

Compounding is annual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 1 for M.

(EFF%)=(1+0.051)1−1.0=0.05=5%

So, effective annual rate for Bank A is 5%.

Given for Bank B,

Nominal interest rate is 5%.

Compounding is semiannual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 2 for M.

(EFF%)=(1+0.052)2−1.0=0.0506=5.06%

So,effective annual rate for Bank B is 5.06%.

Given for Bank C,

Nominal interest rate is 5%.

Compounding is quarterly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 4 for M.

(EFF%)=(1+0.054)4−1.0=0.0509=5.09%

So, effective annual rate for Bank C is 5.09%.

Given for Bank D,

Nominal interest rate is 5%.

Compounding ismonthly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 12 for M.

(EFF%)=(1+0.0512)12−1.0=0.0511=5.11%

So, effective annual rate for Bank D is 5.11%.

Given for Bank E,

Nominal interest rate is 5%.

Compounding is daily.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 365 for M.

(EFF%)=(1+0.05365)365−1.0=0.0512=5.12%

So, effective annual rate for Bank E is 5.12%.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 16

Table (16)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 250, $5,253,$5,254.50, $5,255.50 and $5,256.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 17

Table (17)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 512, $5,518.80, $5,521.95, $5,524.06 and $5,525.11.

Conclusion

Each bank pays different effective rate as there compounding is different, the rates are5% for bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E, also the future values also change on the basis of their number of periods.

2.

Summary Introduction

To explain: If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

2.

Expert Solution

Answer to Problem 41SP

No, it is not possible for the banks to equally attract funds.

The nominal rate which causes same effective rate for all banks are,

Particulars	A	B	C	D	E
Nominalrate	5%	5.06%	5.09%	5.11%	5.12%

Table (18)

Explanation of Solution

Bank will not be equally able to attract funds because of compounding, as people prefer to invest in that bank which have more frequent compounding in comparison to the bank which have lesser frequent compounding.
Nominal rate is opposite of the effective rate which is calculated in part ‘1’. The nominal rate indicated in above table will cause same effective rate for all banks as it is for A bank.

Conclusion

Due to frequent compounding, banks will not be able to equally attract funds and the nominal rate will be 5% for Bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E.

3.

Summary Introduction

To calculate: Present value of amount to get $5,000 after 1 year.

3.

Expert Solution

Explanation of Solution

Calculation of payment to be made in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 18

Table (19)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

So, the amounts to be paid are$4,761.90,$2498.10,$1,102.40,$296.96 and $15.83.

4.

Summary Introduction

To explain: If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

4.

Expert Solution

Answer to Problem 41SP

Yes, a rational investor would be indifferent between the banks.

Explanation of Solution

Rational investor chooses the bank which will provide him better return so he would be indifferent, if all the banks are giving same effective rate because he chooses the bank which will have more frequent compounding than others.

Conclusion

A bank offers frequent compounding is able to attract more number of customers than others.

Summary Introduction

To prepare: Amortization schedule to show annual payments, interest payments, principal payments, and beginning and ending loan balances.

Amortization:

Amotization means to write off or pay the debt over the priod of time it can be for loan or intangible assets. Its main purpose is to get cost recovery. Example of amortization is ,an automobile company that spent $20 million dollars on a design patent with a useful life of 20 years. The amortization value for that company will be $1 million each year.

Expert Solution

Explanation of Solution

Calculation of annual installment is done by using “PMT” formula in spreadsheet at the amortization schedule.

Amortization schedule is prepared below,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 19

Table (20)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

Amortization schedule represents annual payments, interest payments, principal payments, and beginning and ending loan balances.

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Answer 5

Chapter 5, Problem 41SP

a.

Summary Introduction

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

a.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 1

Table (1)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,610.50.

Conclusion

Future value of $1,000 is $1,610.51.

b.

Summary Introduction

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

b.

Expert Solution

Explanation of Solution

Calculation spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 2

Table (2)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in required field.

Conclusion

Investment future values are different for the different years with 0%, 5% and 20% interest rate.

c.

Summary Introduction

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

c.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 3

Table (3)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $620.92.

Conclusion

Present value of $1,000 is $620.92 at 10 % discount rate.

d.

Summary Introduction

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

d.

Expert Solution

Explanation of Solution

Calculationin spreadsheet by “RATE” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 4

Table (4)

Steps required to calculate present value by using “RATE” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “RATE” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 14.87%

Conclusion

The rate of return is14.87%.

e.

Summary Introduction

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2%

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

e.

Expert Solution

Explanation of Solution

Calculation is solved in spreadsheet by “NPER” formula

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 5

Table (5)

Steps required to calculate present value by using “NPER” function in excel are given,

Select ‘Formulas’ option from Menu Bar of excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPER” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 35 years.

Conclusion

Conclusion:

It will take 35 years to double the population from 36.5 million to 73 million.

f.

Summary Introduction

To calculate: Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

f.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 6

Table (6)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,352.16.

So, the present value is $3,352.16.

Calculation of future value of annuity in spreadsheet by using “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 7

Table (7)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $6,742.38.

So the future value is $6,742.38.

Conclusion

Present value is $3,352.16 and future value is $6,742.38 of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

g.

Summary Introduction

To calculate: Present and future value of part ‘f’ if the annuity is due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

g.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 8

Table (8)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,351.66.

Present value of annuity due is $3,351.66.

Future value of annuity in spreadsheet by “FV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 9

Table (9)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $7,753.74

Future value of annuity due is $7,753.74.

Conclusion

Present value of annuity due is $3,351.66 while future value is $7,753.74.

h.

Summary Introduction

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

h.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 10

Table (10)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $613.91.

Present value is $613.91.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 11

Table (11)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Future value of annuity is $1,628.89.

Conclusion

Present andfuture value for $1,000, due in 5 years with 10% semiannual compoundingwill be $613.91 and $1,628.89, respectively.

i.

Summary Introduction

To calculate: Annual payments for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

i.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 12

Table (12)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity is $149.03.

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 13

Table (13)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity due is $137.99.

Conclusion

Annual payments are$149.03 for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due is $137.99.

j.

Summary Introduction

To calculate: Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

j.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “NPV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 14

Table (14)

Steps required to calculate present value by using “NPV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $581.59.

Present value is $581.59.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 15

Table (15)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $732.54.

Future value is $732.54.

Conclusion

Present value is $581.89 while future value is $732.54.

k.1.

Summary Introduction

To calculate: Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

k.1.

Expert Solution

Explanation of Solution

Given for Bank A,

Nominal interest rate is 5%.

Compounding is annual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 1 for M.

(EFF%)=(1+0.051)1−1.0=0.05=5%

So, effective annual rate for Bank A is 5%.

Given for Bank B,

Nominal interest rate is 5%.

Compounding is semiannual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 2 for M.

(EFF%)=(1+0.052)2−1.0=0.0506=5.06%

So,effective annual rate for Bank B is 5.06%.

Given for Bank C,

Nominal interest rate is 5%.

Compounding is quarterly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 4 for M.

(EFF%)=(1+0.054)4−1.0=0.0509=5.09%

So, effective annual rate for Bank C is 5.09%.

Given for Bank D,

Nominal interest rate is 5%.

Compounding ismonthly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 12 for M.

(EFF%)=(1+0.0512)12−1.0=0.0511=5.11%

So, effective annual rate for Bank D is 5.11%.

Given for Bank E,

Nominal interest rate is 5%.

Compounding is daily.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 365 for M.

(EFF%)=(1+0.05365)365−1.0=0.0512=5.12%

So, effective annual rate for Bank E is 5.12%.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 16

Table (16)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 250, $5,253,$5,254.50, $5,255.50 and $5,256.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 17

Table (17)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 512, $5,518.80, $5,521.95, $5,524.06 and $5,525.11.

Conclusion

Each bank pays different effective rate as there compounding is different, the rates are5% for bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E, also the future values also change on the basis of their number of periods.

2.

Summary Introduction

To explain: If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

2.

Expert Solution

Answer to Problem 41SP

No, it is not possible for the banks to equally attract funds.

The nominal rate which causes same effective rate for all banks are,

Particulars	A	B	C	D	E
Nominalrate	5%	5.06%	5.09%	5.11%	5.12%

Table (18)

Explanation of Solution

Bank will not be equally able to attract funds because of compounding, as people prefer to invest in that bank which have more frequent compounding in comparison to the bank which have lesser frequent compounding.
Nominal rate is opposite of the effective rate which is calculated in part ‘1’. The nominal rate indicated in above table will cause same effective rate for all banks as it is for A bank.

Conclusion

Due to frequent compounding, banks will not be able to equally attract funds and the nominal rate will be 5% for Bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E.

3.

Summary Introduction

To calculate: Present value of amount to get $5,000 after 1 year.

3.

Expert Solution

Explanation of Solution

Calculation of payment to be made in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 18

Table (19)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

So, the amounts to be paid are$4,761.90,$2498.10,$1,102.40,$296.96 and $15.83.

4.

Summary Introduction

To explain: If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

4.

Expert Solution

Answer to Problem 41SP

Yes, a rational investor would be indifferent between the banks.

Explanation of Solution

Rational investor chooses the bank which will provide him better return so he would be indifferent, if all the banks are giving same effective rate because he chooses the bank which will have more frequent compounding than others.

Conclusion

A bank offers frequent compounding is able to attract more number of customers than others.

Summary Introduction

To prepare: Amortization schedule to show annual payments, interest payments, principal payments, and beginning and ending loan balances.

Amortization:

Amotization means to write off or pay the debt over the priod of time it can be for loan or intangible assets. Its main purpose is to get cost recovery. Example of amortization is ,an automobile company that spent $20 million dollars on a design patent with a useful life of 20 years. The amortization value for that company will be $1 million each year.

Expert Solution

Explanation of Solution

Calculation of annual installment is done by using “PMT” formula in spreadsheet at the amortization schedule.

Amortization schedule is prepared below,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 19

Table (20)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

Amortization schedule represents annual payments, interest payments, principal payments, and beginning and ending loan balances.

Answer 6

Chapter 5, Problem 41SP

a.

Summary Introduction

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

a.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 1

Table (1)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,610.50.

Conclusion

Future value of $1,000 is $1,610.51.

Answer 7

Chapter 5, Problem 41SP

a.

Summary Introduction

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 8

a.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 1

Table (1)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,610.50.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Conclusion

Future value of $1,000 is $1,610.51.

Answer 13

b.

Summary Introduction

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

b.

Expert Solution

Explanation of Solution

Calculation spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 2

Table (2)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in required field.

Conclusion

Investment future values are different for the different years with 0%, 5% and 20% interest rate.

Answer 14

b.

Summary Introduction

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 15

b.

Expert Solution

Explanation of Solution

Calculation spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 2

Table (2)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in required field.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Conclusion

Investment future values are different for the different years with 0%, 5% and 20% interest rate.

Answer 20

c.

Summary Introduction

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

c.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 3

Table (3)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $620.92.

Conclusion

Present value of $1,000 is $620.92 at 10 % discount rate.

Answer 21

c.

Summary Introduction

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 22

c.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 3

Table (3)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $620.92.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Conclusion

Present value of $1,000 is $620.92 at 10 % discount rate.

Answer 27

d.

Summary Introduction

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

d.

Expert Solution

Explanation of Solution

Calculationin spreadsheet by “RATE” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 4

Table (4)

Steps required to calculate present value by using “RATE” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “RATE” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 14.87%

Conclusion

The rate of return is14.87%.

Answer 28

d.

Summary Introduction

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 29

d.

Expert Solution

Explanation of Solution

Calculationin spreadsheet by “RATE” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 4

Table (4)

Steps required to calculate present value by using “RATE” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “RATE” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 14.87%

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Conclusion

The rate of return is14.87%.

Answer 34

e.

Summary Introduction

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2%

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

e.

Expert Solution

Explanation of Solution

Calculation is solved in spreadsheet by “NPER” formula

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 5

Table (5)

Steps required to calculate present value by using “NPER” function in excel are given,

Select ‘Formulas’ option from Menu Bar of excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPER” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 35 years.

Conclusion

Conclusion:

It will take 35 years to double the population from 36.5 million to 73 million.

Answer 35

e.

Summary Introduction

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2%

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 36

e.

Expert Solution

Explanation of Solution

Calculation is solved in spreadsheet by “NPER” formula

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 5

Table (5)

Steps required to calculate present value by using “NPER” function in excel are given,

Select ‘Formulas’ option from Menu Bar of excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPER” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is 35 years.

Answer 37

e.

Expert Solution

Answer 38

e.

Expert Solution

Answer 39

Expert Solution

Answer 40

Conclusion

Conclusion:

It will take 35 years to double the population from 36.5 million to 73 million.

Answer 41

f.

Summary Introduction

To calculate: Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

f.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 6

Table (6)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,352.16.

So, the present value is $3,352.16.

Calculation of future value of annuity in spreadsheet by using “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 7

Table (7)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $6,742.38.

So the future value is $6,742.38.

Conclusion

Present value is $3,352.16 and future value is $6,742.38 of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Answer 42

f.

Summary Introduction

To calculate: Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 43

f.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 6

Table (6)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,352.16.

So, the present value is $3,352.16.

Calculation of future value of annuity in spreadsheet by using “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 7

Table (7)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $6,742.38.

So the future value is $6,742.38.

Answer 44

f.

Expert Solution

Answer 45

f.

Expert Solution

Answer 46

Expert Solution

Answer 47

Conclusion

Present value is $3,352.16 and future value is $6,742.38 of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

Answer 48

g.

Summary Introduction

To calculate: Present and future value of part ‘f’ if the annuity is due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

g.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 8

Table (8)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,351.66.

Present value of annuity due is $3,351.66.

Future value of annuity in spreadsheet by “FV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 9

Table (9)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $7,753.74

Future value of annuity due is $7,753.74.

Conclusion

Present value of annuity due is $3,351.66 while future value is $7,753.74.

Answer 49

g.

Summary Introduction

To calculate: Present and future value of part ‘f’ if the annuity is due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 50

g.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 8

Table (8)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $3,351.66.

Present value of annuity due is $3,351.66.

Future value of annuity in spreadsheet by “FV” function,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 9

Table (9)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $7,753.74

Future value of annuity due is $7,753.74.

Answer 51

g.

Expert Solution

Answer 52

g.

Expert Solution

Answer 53

Expert Solution

Answer 54

Conclusion

Present value of annuity due is $3,351.66 while future value is $7,753.74.

Answer 55

h.

Summary Introduction

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

h.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 10

Table (10)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $613.91.

Present value is $613.91.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 11

Table (11)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Future value of annuity is $1,628.89.

Conclusion

Present andfuture value for $1,000, due in 5 years with 10% semiannual compoundingwill be $613.91 and $1,628.89, respectively.

Answer 56

h.

Summary Introduction

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 57

h.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 10

Table (10)

Steps required to calculate present value by using “PV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $613.91.

Present value is $613.91.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 11

Table (11)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Future value of annuity is $1,628.89.

Answer 58

h.

Expert Solution

Answer 59

h.

Expert Solution

Answer 60

Expert Solution

Answer 61

Conclusion

Present andfuture value for $1,000, due in 5 years with 10% semiannual compoundingwill be $613.91 and $1,628.89, respectively.

Answer 62

i.

Summary Introduction

To calculate: Annual payments for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

i.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 12

Table (12)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity is $149.03.

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 13

Table (13)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity due is $137.99.

Conclusion

Annual payments are$149.03 for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due is $137.99.

Answer 63

i.

Summary Introduction

To calculate: Annual payments for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Answer 64

i.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 12

Table (12)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity is $149.03.

Calculation in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 13

Table (13)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $1,628.89.

Payment of ordinary annuity due is $137.99.

Answer 65

i.

Expert Solution

Answer 66

i.

Expert Solution

Answer 67

Expert Solution

Answer 68

Conclusion

Annual payments are$149.03 for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due is $137.99.

Answer 69

j.

Summary Introduction

To calculate: Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

j.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “NPV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 14

Table (14)

Steps required to calculate present value by using “NPV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $581.59.

Present value is $581.59.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 15

Table (15)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $732.54.

Future value is $732.54.

Conclusion

Present value is $581.89 while future value is $732.54.

Answer 70

j.

Summary Introduction

To calculate: Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

Answer 71

j.

Expert Solution

Explanation of Solution

Calculation in spreadsheet by “NPV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 14

Table (14)

Steps required to calculate present value by using “NPV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “NPV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $581.59.

Present value is $581.59.

Calculation in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 15

Table (15)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.
Final answer will be shown by the formula that is $732.54.

Future value is $732.54.

Answer 72

j.

Expert Solution

Answer 73

j.

Expert Solution

Answer 74

Expert Solution

Answer 75

Conclusion

Present value is $581.89 while future value is $732.54.

Answer 76

k.1.

Summary Introduction

To calculate: Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

k.1.

Expert Solution

Explanation of Solution

Given for Bank A,

Nominal interest rate is 5%.

Compounding is annual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 1 for M.

(EFF%)=(1+0.051)1−1.0=0.05=5%

So, effective annual rate for Bank A is 5%.

Given for Bank B,

Nominal interest rate is 5%.

Compounding is semiannual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 2 for M.

(EFF%)=(1+0.052)2−1.0=0.0506=5.06%

So,effective annual rate for Bank B is 5.06%.

Given for Bank C,

Nominal interest rate is 5%.

Compounding is quarterly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 4 for M.

(EFF%)=(1+0.054)4−1.0=0.0509=5.09%

So, effective annual rate for Bank C is 5.09%.

Given for Bank D,

Nominal interest rate is 5%.

Compounding ismonthly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 12 for M.

(EFF%)=(1+0.0512)12−1.0=0.0511=5.11%

So, effective annual rate for Bank D is 5.11%.

Given for Bank E,

Nominal interest rate is 5%.

Compounding is daily.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 365 for M.

(EFF%)=(1+0.05365)365−1.0=0.0512=5.12%

So, effective annual rate for Bank E is 5.12%.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 16

Table (16)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 250, $5,253,$5,254.50, $5,255.50 and $5,256.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 17

Table (17)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 512, $5,518.80, $5,521.95, $5,524.06 and $5,525.11.

Conclusion

Each bank pays different effective rate as there compounding is different, the rates are5% for bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E, also the future values also change on the basis of their number of periods.

Answer 77

k.1.

Summary Introduction

To calculate: Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

Answer 78

k.1.

Expert Solution

Explanation of Solution

Given for Bank A,

Nominal interest rate is 5%.

Compounding is annual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 1 for M.

(EFF%)=(1+0.051)1−1.0=0.05=5%

So, effective annual rate for Bank A is 5%.

Given for Bank B,

Nominal interest rate is 5%.

Compounding is semiannual.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 2 for M.

(EFF%)=(1+0.052)2−1.0=0.0506=5.06%

So,effective annual rate for Bank B is 5.06%.

Given for Bank C,

Nominal interest rate is 5%.

Compounding is quarterly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 4 for M.

(EFF%)=(1+0.054)4−1.0=0.0509=5.09%

So, effective annual rate for Bank C is 5.09%.

Given for Bank D,

Nominal interest rate is 5%.

Compounding ismonthly.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 12 for M.

(EFF%)=(1+0.0512)12−1.0=0.0511=5.11%

So, effective annual rate for Bank D is 5.11%.

Given for Bank E,

Nominal interest rate is 5%.

Compounding is daily.

Formula to calculate effective annual rate is,

(EFF%)=(1+INOMM)M−1.0

Where,

EFF is the effective annual rate.
I_NOM is the nominal interest rate.
M is the compounding period.

Substitute 5% for I_NOM and 365 for M.

(EFF%)=(1+0.05365)365−1.0=0.0512=5.12%

So, effective annual rate for Bank E is 5.12%.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 16

Table (16)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 250, $5,253,$5,254.50, $5,255.50 and $5,256.

Calculation of future value in spreadsheet by “FV” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 17

Table (17)

Steps required to calculate present value by using “FV” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “FV” and then press OK.
A window will pop up.
Input data in the required field.

So, the future value at different effective rate after a year are $5, 512, $5,518.80, $5,521.95, $5,524.06 and $5,525.11.

Answer 79

k.1.

Expert Solution

Answer 80

k.1.

Expert Solution

Answer 81

Expert Solution

Answer 82

Conclusion

Each bank pays different effective rate as there compounding is different, the rates are5% for bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E, also the future values also change on the basis of their number of periods.

Answer 83

2.

Summary Introduction

To explain: If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

2.

Expert Solution

Answer to Problem 41SP

No, it is not possible for the banks to equally attract funds.

The nominal rate which causes same effective rate for all banks are,

Particulars	A	B	C	D	E
Nominalrate	5%	5.06%	5.09%	5.11%	5.12%

Table (18)

Explanation of Solution

Bank will not be equally able to attract funds because of compounding, as people prefer to invest in that bank which have more frequent compounding in comparison to the bank which have lesser frequent compounding.
Nominal rate is opposite of the effective rate which is calculated in part ‘1’. The nominal rate indicated in above table will cause same effective rate for all banks as it is for A bank.

Conclusion

Due to frequent compounding, banks will not be able to equally attract funds and the nominal rate will be 5% for Bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E.

Answer 84

2.

Summary Introduction

To explain: If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

Answer 85

2.

Expert Solution

Answer to Problem 41SP

No, it is not possible for the banks to equally attract funds.

The nominal rate which causes same effective rate for all banks are,

Particulars	A	B	C	D	E
Nominalrate	5%	5.06%	5.09%	5.11%	5.12%

Table (18)

Answer 86

2.

Expert Solution

Answer 87

2.

Expert Solution

Answer 88

Expert Solution

Answer 89

Explanation of Solution

Bank will not be equally able to attract funds because of compounding, as people prefer to invest in that bank which have more frequent compounding in comparison to the bank which have lesser frequent compounding.
Nominal rate is opposite of the effective rate which is calculated in part ‘1’. The nominal rate indicated in above table will cause same effective rate for all banks as it is for A bank.

Answer 90

Conclusion

Due to frequent compounding, banks will not be able to equally attract funds and the nominal rate will be 5% for Bank A, 5.06% Bank B, 5.09% Bank C, 5.11% Bank D, 5.12% Bank E.

Answer 91

3.

Summary Introduction

To calculate: Present value of amount to get $5,000 after 1 year.

3.

Expert Solution

Explanation of Solution

Calculation of payment to be made in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 18

Table (19)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

So, the amounts to be paid are$4,761.90,$2498.10,$1,102.40,$296.96 and $15.83.

Answer 92

3.

Summary Introduction

To calculate: Present value of amount to get $5,000 after 1 year.

Answer 93

3.

Expert Solution

Explanation of Solution

Calculation of payment to be made in spreadsheet by “PMT” formula,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 18

Table (19)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Answer 94

3.

Expert Solution

Answer 95

3.

Expert Solution

Answer 96

Expert Solution

Answer 97

Conclusion

So, the amounts to be paid are$4,761.90,$2498.10,$1,102.40,$296.96 and $15.83.

Answer 98

4.

Summary Introduction

To explain: If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

4.

Expert Solution

Answer to Problem 41SP

Yes, a rational investor would be indifferent between the banks.

Explanation of Solution

Rational investor chooses the bank which will provide him better return so he would be indifferent, if all the banks are giving same effective rate because he chooses the bank which will have more frequent compounding than others.

Conclusion

A bank offers frequent compounding is able to attract more number of customers than others.

Answer 99

4.

Summary Introduction

To explain: If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

Answer 100

4.

Expert Solution

Answer to Problem 41SP

Yes, a rational investor would be indifferent between the banks.

Answer 101

4.

Expert Solution

Answer 102

4.

Expert Solution

Answer 103

Expert Solution

Answer 104

Explanation of Solution

Rational investor chooses the bank which will provide him better return so he would be indifferent, if all the banks are giving same effective rate because he chooses the bank which will have more frequent compounding than others.

Answer 105

Conclusion

A bank offers frequent compounding is able to attract more number of customers than others.

Answer 106

Summary Introduction

To prepare: Amortization schedule to show annual payments, interest payments, principal payments, and beginning and ending loan balances.

Amortization:

Amotization means to write off or pay the debt over the priod of time it can be for loan or intangible assets. Its main purpose is to get cost recovery. Example of amortization is ,an automobile company that spent $20 million dollars on a design patent with a useful life of 20 years. The amortization value for that company will be $1 million each year.

Expert Solution

Explanation of Solution

Calculation of annual installment is done by using “PMT” formula in spreadsheet at the amortization schedule.

Amortization schedule is prepared below,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 19

Table (20)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Conclusion

Amortization schedule represents annual payments, interest payments, principal payments, and beginning and ending loan balances.

Answer 107

Summary Introduction

To prepare: Amortization schedule to show annual payments, interest payments, principal payments, and beginning and ending loan balances.

Amortization:

Amotization means to write off or pay the debt over the priod of time it can be for loan or intangible assets. Its main purpose is to get cost recovery. Example of amortization is ,an automobile company that spent $20 million dollars on a design patent with a useful life of 20 years. The amortization value for that company will be $1 million each year.

Answer 108

Expert Solution

Explanation of Solution

Calculation of annual installment is done by using “PMT” formula in spreadsheet at the amortization schedule.

Amortization schedule is prepared below,

Fundamentals of Financial Management, Concise Edition, Chapter 5, Problem 41SP , additional homework tip 19

Table (20)

Steps required to calculate present value by using “PMT” function in excel are given,

Select ‘Formulas’ option from Menu Bar of Excel sheet.
Select insert Function that is (fx).
Choose category of Financial.
Then select “PMT” and then press OK.
A window will pop up.
Input data in the required field.

Answer 109

Expert Solution

Answer 110

Expert Solution

Answer 111

Expert Solution

Answer 112

Conclusion

Amortization schedule represents annual payments, interest payments, principal payments, and beginning and ending loan balances.

Answer 113

Ch. 5 - Prob. 1Q Ch. 5 - Explain whether the following statement is true or...Ch. 5 - If a firms earnings per share grew from 1 to 2...Ch. 5 - Would you rather have a savings account that pays...Ch. 5 - Prob. 5Q Ch. 5 - Prob. 6Q Ch. 5 - Banks and other lenders are required to disclose a...Ch. 5 - Prob. 8Q Ch. 5 - Prob. 1P Ch. 5 - PRESENT VALUE What is the present value of a...

Future value of $1,000 after 5 years at 10% annual interest rate. Introduction: Time Value of Money : It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate. Introduction: Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation of Solution

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years. Introduction: Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation of Solution

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%. Introduction: Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation of Solution

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years. Introduction: Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation of Solution

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2% Introduction: Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation of Solution

To calculate: Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%. Introduction: Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation of Solution

To calculate: Present and future value of part ‘f’ if the annuity is due. Introduction: Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation of Solution

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding. Introduction: Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation of Solution

Explanation of Solution

To calculate: Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

Explanation of Solution

To calculate: Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

Explanation of Solution

To explain: If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

Answer to Problem 41SP

Explanation of Solution

To calculate: Present value of amount to get $5,000 after 1 year.

Explanation of Solution

To explain: If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

Answer to Problem 41SP

Explanation of Solution

Explanation of Solution

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Chapter 5 Solutions

To calculate: Future value of $1,000 after 5 years at 10% annual interest rate.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

To calculate: Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

To calculate: Present value due of $1,000 in 5 years at the discount rate of 10%.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

To calculate: Rate of return of security $1,000 and returns as $2,000 after 5 years.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

To calculate: Time taken by 36.5 million populations to double with annual growth rate of 2%

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

To calculate: Present and future value of part ‘f’ if the annuity is due.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

To calculate: Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

Introduction:

Time Value of Money: It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.