Fundamentals of Financial Management, Concise Edition
Fundamentals of Financial Management, Concise Edition
9th Edition
ISBN: 9781337087544
Author: Eugene F. Brigham, Joel F. Houston
Publisher: Cengage Learning
Question
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Chapter 5, Problem 14P

a.

Summary Introduction

To calculate: Future value of annuity of $500 for a year for 8 years at 14%

Annuity:

It is an agreement under which person pays the lump sum payment or number of small payments and in return gets the amount at later date or upon annuitization. The purpose of the annuity is   not to break the flow of income after retirement.

a.

Expert Solution
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Explanation of Solution

Given,

The annuity is $500 per year.

The interest rate is 14% or 0.14.

The numbers of years are 8 years.

The formula to calculate value of annuity is equation (I).

FVAnnuity=C×((1+i)n-1i)

Here,

  • FV stands for future value.
  • C is for monthly payment.
  • I is interest rate.
  • n stands for no of payments.

Substitute $500 for C, 0.14 , n for 8 years in equation (I)

FV=$500((1+0.14)810.14)=$500×1.850.14=$500×13.21=$6,605

The annuity is $6,605.

Conclusion

Hence, the future value of annuity is $6,605.

(b)

Summary Introduction

To calculate: Future value of annuity of $250 for a year for 4 years at 7%

Annuity:

It is an agreement under which person pays the lump sum payment or number of small payments and in return gets the amount at later date or upon annuitization. The purpose of the annuity is   not to break the flow of income after retirement.

(b)

Expert Solution
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Explanation of Solution

Given,

The annuity is $250 per year.

The interest rate is 7%.

The numbers of years are 4 years.

Substitute $250 for C, 0.07 , n for 4 years in equation (I)

FV=$250((1+0.07)410.07)=$250×0.3110.07=$250×4.44=$1,110.

Conclusion

The future value of annuity will be $1,110.

(c)

Summary Introduction

To calculate: Future value of annuity of $700 for a year for 4 years at 0%

Annuity:

It is an agreement under which person pays the lump sum payment or number of small payments and in return gets the amount at later date or upon annuitization. The purpose of the annuity is   not to break the flow of income after retirement.

(c)

Expert Solution
Check Mark

Explanation of Solution

Given,

The annuity is $700 per year.

The interest rate is 0%.

The numbers of years are 4 years.

The formula to calculate the future value of an annuity when interest rate is 0,

FV=C×(1+i)n

Substitute $700 for C, 0.00 for r, n for 4 years.

FV=$700×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)=700×5=3500

Conclusion

The future value of annuity will be $3500

(d)

Summary Introduction

To rework: Part a, b and c as they are due.

Annuity:

It is an agreement under which person pays the lump sum payment or number of small payments and in return gets the amount at later date or upon annuitization. The purpose of the annuity is   not to break the flow of income after retirement.

(d)

Expert Solution
Check Mark

Explanation of Solution

The formula to calculate future value of annuity due,

FVAnnuity=C((1+i)n1i)×(1+i)

Were,

  • FV stands for future value of annuity.
  • C symbolizes the monthly payment.
  • I is for interest rate.
  • N is for number of payments.

d .a

Summary Introduction

To calculate: Future value of annuity of $500 for a year for 8 years at 14%

Annuity:

It is an agreement under which person pays the lump sum payment or number of small payments and in return gets the amount at later date or upon annuitization. The purpose of the annuity is   not to break the flow of income after retirement.

d .a

Expert Solution
Check Mark

Explanation of Solution

Given,

The annuity is $500 per year.

The interest rate is 14% or 0.14.

The numbers of years are 8 years.

Substitute C for $500, i for 14%, n for 8 years in equation {(d) I}

FV=$500×((1+0.14)81)0.14×(1+0.14)=$500×15.09=$7,545

Conclusion

The future value of annuity due is $7,545.

b

Summary Introduction

To calculate: Future value of annuity of $250 for a year for 4 years at 7%

Annuity:

It is an agreement under which person pays the lump sum payment or number of small payments and in return gets the amount at later date or upon annuitization. The purpose of the annuity is   not to break the flow of income after retirement.

b

Expert Solution
Check Mark

Explanation of Solution

Given,

The annuity is $250 per year.

The interest rate is 7%.

The numbers of years are 4 years.

Substitute C for $250, I for 7%, n for 4 years.

FV=$250((1+0.07)41)0.07×(1+0.07)=$250×4.75=$1,187.68

Conclusion

The future value of annuity due is $1,187.68.

c

Summary Introduction

To calculate: Future value of annuity of $700 for a year for 4 years at 0%

Annuity:

It is an agreement under which person pays the lump sum payment or number of small payments and in return gets the amount at later date or upon annuitization. The purpose of the annuity is   not to break the flow of income after retirement.

c

Expert Solution
Check Mark

Explanation of Solution

Given,

The annuity is $700 per year.

The interest rate is 0%.

The numbers of years are 4 years.

The following formula will be used to solve.

FVAnnuity=C×(1+i)n×(1+i)

Substitute C for $700, i for 0%, n for 4 years in equation.

FV=$700×((1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)×(1+0.00)=700×5=3,500

Conclusion

The future value of annuity due is $3,500.

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Chapter 5 Solutions

Fundamentals of Financial Management, Concise Edition

Ch. 5 - FINDING THE REQUIRED INTEREST RATE Your parents...Ch. 5 - Prob. 4PCh. 5 - TIME TO REACH A FINANCIAL GOAL You have 33,556.25...Ch. 5 - Prob. 6PCh. 5 - PRESENT AND FUTURE VALUES OF A CASH FLOW STREAM An...Ch. 5 - LOAN AMORTIZATION AND EAR You want to buy a car,...Ch. 5 - Prob. 9PCh. 5 - PRESENT AND FUTURE VALUES FOR DIFFERENT INTEREST...Ch. 5 - GROWTH RATES Sawyer Corporations 2015 sales were 5...Ch. 5 - EFFECTIVE RATE OF INTEREST Find the interest rates...Ch. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - PRESENT VALUE OF AN ANNUITY Find the present...Ch. 5 - Prob. 16PCh. 5 - EFFECTIVE INTEREST RATE You borrow 230,000; the...Ch. 5 - Prob. 18PCh. 5 - FUTURE VALUE OF AN ANNUITY Your client is 26 years...Ch. 5 - Prob. 20PCh. 5 - EVALUATING LUMP SUMS AND ANNUITIES Kristina just...Ch. 5 - LOAN AMORTIZATION Jan sold her house on December...Ch. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - PV AND LOAN ELIGIBILITY You have saved 4,000 for a...Ch. 5 - EFFECTIVE VERSUS NOMINAL INTEREST RATES Bank A...Ch. 5 - NOMINAL INTEREST RATE AND EXTENDING CREDIT As a...Ch. 5 - BUILDING CREDIT COST INTO PRICES Your firm sells...Ch. 5 - Prob. 30PCh. 5 - REQUIRED LUMP SUM PAYMENT Starting next year, you...Ch. 5 - REACHING A FINANCIAL GOAL Six years from today you...Ch. 5 - FV OF UNEVEN CASH FLOW You want to buy a house...Ch. 5 - AMORTIZATION SCHEDULE a. Set up an amortization...Ch. 5 - AMORTIZATION SCHEDULE WITH A BALLOON PAYMENT You...Ch. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - Prob. 38PCh. 5 - Prob. 39PCh. 5 - REQUIRED ANNUITY PAYMENTS A father is now planning...Ch. 5 - Prob. 41SPCh. 5 - Prob. 42IC
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