The annual percentage rate and the effective annual rate Introduction: The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 6, Problem 77QP

a)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

a)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 390%, the effective annual rate is 4,197.74%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Compute the annual percentage rate:

APR=52(7.5%)=390%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 390%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.075)52−1=42.9774−1=41.9774

Hence, the effective annual rate is 0.41,9774 or 4,197.74%

b)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

b)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 421.62%, the effective annual rate is 5,662.75%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay back the full principal value. With the discount of 7.5%, Person X receives $9.25 for each $10 as the principal value. The weekly interest rates are calculated as follows:

$10=$9.25(1+r)r=($10$9.25)−1r=1.0811−1r=0.0811

Note: The dollar values that are used above are not relevant. In other words, it can also be written as $0.925 and $1 or $92.5 and $100 or in any other combination that provides similar rate of interest.

Hence, the r value is 0.0811 or 8.11%

Compute the annual percentage rate:

APR=52(8.11%)=421.62%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 421.62%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.0811)52−1=57.6275−1=56.6275

Hence, the effective annual rate is 56.6275 or 5,662.75%

c)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

c)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 968.19%, the effective annual rate is 717,745.21%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In this part, the present value of an annuity and the cash flow is given; with the help of the present value of annuity equation, the r value is found using a spreadsheet.

Formula to calculate the present value annuity:

Present value annuity=C{[1−(11+rt)]r}

Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. Using the formulae of the present value of annuity, the interest rate is computed using the spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$66.45=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 1

Type the formulae of the present value annuity in H6 in the spreadsheet and consider the r value as H7

Step 2:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 3

In the spreadsheet, go to Data and select What-If-Analysis.
Under What-If-Analysis, select Goal Seek
In set cell, select H6 (the formula)
The To value is considered as 66.45 (the value of the present value of annuity)
The H7 cell is selected for the 'by changing cell.'

Step 4:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 4

Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value

Step 5:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 5

The r value appears to be 18.6190266505771%

Hence, the r value is 18.62%

Compute the annual percentage rate:

APR=52(18.62%)=968.19%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of periods in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 968.19%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.1862)52−1=7,178.4521−1=7,177.4521

Hence, the effective annual rate is 7,177.4521 or 717,745.21%.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

What are the implications of missing a credit card payment in finance?

Omni Advisors, an international pension fund manager, uses the concepts of purchasing power parity (PPP) and the International Fisher Effect (IFE) to forecast spot exchange rates. Omni gathers the financial information as follows: Base price level 100 Current U.S. price level 105 Current South African price level 111 Base rand spot exchange rate $ 0.188 Current rand spot exchange rate $ 0.171 Expected annual U.S. inflation 7% Expected annual South African inflation 5% Expected U.S. one-year interest rate 10% Expected South African one-year interest rate 8% Required: a. The current ZAR spot rate in USD that would have been forecast by PPP.Note: Do not round intermediate calculations. Round your answer to 4 decimal places. b. Using the IFE, the expected ZAR spot rate in USD one year from now.Note: Do not round intermediate calculations. Round your answer to 4 decimal places. c. Using PPP, the expected ZAR spot rate in USD four years from now.Note: Do not round intermediate calculations.…

Delta Company, a U.S. MNC, is contemplating making a foreign capital expenditure in South Africa. The initial cost of the project is ZAR11,000. The annual cash flows over the five-year economic life of the project in ZAR are estimated to be 3,300, 4,300, 5,290, 6,280, and 7,250. The parent firm's cost of capital in dollars is 9,5 percent. Long-run inflation is forecasted to be 3 percent per annum in the United States and 7 percent in South Africa. The current spot foreign exchange rate is ZAR per USD = 3.75. Required:. Calculating the NPV in ZAR using the ZAR equivalent cost of capital according to the Fisher effect and then converting to USD at the current spot rate. - NPV in USD using fisher effect Converting all cash flows from ZAR to USD at purchasing power parity forecasted exchange rates and then calculating the NPV at the dollar cost of capital. - NPV in USD using PPP rates Are the two USD NPs different or the same? What is the NPV in dollars if the actual pattern of ZAR per…

Answer 2

Question

Chapter 6, Problem 77QP

a)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

a)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 390%, the effective annual rate is 4,197.74%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Compute the annual percentage rate:

APR=52(7.5%)=390%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 390%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.075)52−1=42.9774−1=41.9774

Hence, the effective annual rate is 0.41,9774 or 4,197.74%

b)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

b)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 421.62%, the effective annual rate is 5,662.75%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay back the full principal value. With the discount of 7.5%, Person X receives $9.25 for each $10 as the principal value. The weekly interest rates are calculated as follows:

$10=$9.25(1+r)r=($10$9.25)−1r=1.0811−1r=0.0811

Note: The dollar values that are used above are not relevant. In other words, it can also be written as $0.925 and $1 or $92.5 and $100 or in any other combination that provides similar rate of interest.

Hence, the r value is 0.0811 or 8.11%

Compute the annual percentage rate:

APR=52(8.11%)=421.62%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 421.62%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.0811)52−1=57.6275−1=56.6275

Hence, the effective annual rate is 56.6275 or 5,662.75%

c)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

c)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 968.19%, the effective annual rate is 717,745.21%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In this part, the present value of an annuity and the cash flow is given; with the help of the present value of annuity equation, the r value is found using a spreadsheet.

Formula to calculate the present value annuity:

Present value annuity=C{[1−(11+rt)]r}

Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. Using the formulae of the present value of annuity, the interest rate is computed using the spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$66.45=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 1

Type the formulae of the present value annuity in H6 in the spreadsheet and consider the r value as H7

Step 2:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 3

In the spreadsheet, go to Data and select What-If-Analysis.
Under What-If-Analysis, select Goal Seek
In set cell, select H6 (the formula)
The To value is considered as 66.45 (the value of the present value of annuity)
The H7 cell is selected for the 'by changing cell.'

Step 4:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 4

Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value

Step 5:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 5

The r value appears to be 18.6190266505771%

Hence, the r value is 18.62%

Compute the annual percentage rate:

APR=52(18.62%)=968.19%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of periods in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 968.19%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.1862)52−1=7,178.4521−1=7,177.4521

Hence, the effective annual rate is 7,177.4521 or 717,745.21%.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 6, Problem 77QP

a)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

a)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 390%, the effective annual rate is 4,197.74%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Compute the annual percentage rate:

APR=52(7.5%)=390%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 390%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.075)52−1=42.9774−1=41.9774

Hence, the effective annual rate is 0.41,9774 or 4,197.74%

b)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

b)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 421.62%, the effective annual rate is 5,662.75%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay back the full principal value. With the discount of 7.5%, Person X receives $9.25 for each $10 as the principal value. The weekly interest rates are calculated as follows:

$10=$9.25(1+r)r=($10$9.25)−1r=1.0811−1r=0.0811

Note: The dollar values that are used above are not relevant. In other words, it can also be written as $0.925 and $1 or $92.5 and $100 or in any other combination that provides similar rate of interest.

Hence, the r value is 0.0811 or 8.11%

Compute the annual percentage rate:

APR=52(8.11%)=421.62%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 421.62%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.0811)52−1=57.6275−1=56.6275

Hence, the effective annual rate is 56.6275 or 5,662.75%

c)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

c)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 968.19%, the effective annual rate is 717,745.21%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In this part, the present value of an annuity and the cash flow is given; with the help of the present value of annuity equation, the r value is found using a spreadsheet.

Formula to calculate the present value annuity:

Present value annuity=C{[1−(11+rt)]r}

Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. Using the formulae of the present value of annuity, the interest rate is computed using the spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$66.45=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 1

Type the formulae of the present value annuity in H6 in the spreadsheet and consider the r value as H7

Step 2:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 3

In the spreadsheet, go to Data and select What-If-Analysis.
Under What-If-Analysis, select Goal Seek
In set cell, select H6 (the formula)
The To value is considered as 66.45 (the value of the present value of annuity)
The H7 cell is selected for the 'by changing cell.'

Step 4:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 4

Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value

Step 5:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 5

The r value appears to be 18.6190266505771%

Hence, the r value is 18.62%

Compute the annual percentage rate:

APR=52(18.62%)=968.19%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of periods in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 968.19%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.1862)52−1=7,178.4521−1=7,177.4521

Hence, the effective annual rate is 7,177.4521 or 717,745.21%.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 6, Problem 77QP

a)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

a)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 390%, the effective annual rate is 4,197.74%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Compute the annual percentage rate:

APR=52(7.5%)=390%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 390%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.075)52−1=42.9774−1=41.9774

Hence, the effective annual rate is 0.41,9774 or 4,197.74%

b)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

b)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 421.62%, the effective annual rate is 5,662.75%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay back the full principal value. With the discount of 7.5%, Person X receives $9.25 for each $10 as the principal value. The weekly interest rates are calculated as follows:

$10=$9.25(1+r)r=($10$9.25)−1r=1.0811−1r=0.0811

Note: The dollar values that are used above are not relevant. In other words, it can also be written as $0.925 and $1 or $92.5 and $100 or in any other combination that provides similar rate of interest.

Hence, the r value is 0.0811 or 8.11%

Compute the annual percentage rate:

APR=52(8.11%)=421.62%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 421.62%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.0811)52−1=57.6275−1=56.6275

Hence, the effective annual rate is 56.6275 or 5,662.75%

c)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

c)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 968.19%, the effective annual rate is 717,745.21%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In this part, the present value of an annuity and the cash flow is given; with the help of the present value of annuity equation, the r value is found using a spreadsheet.

Formula to calculate the present value annuity:

Present value annuity=C{[1−(11+rt)]r}

Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. Using the formulae of the present value of annuity, the interest rate is computed using the spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$66.45=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 1

Type the formulae of the present value annuity in H6 in the spreadsheet and consider the r value as H7

Step 2:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 3

In the spreadsheet, go to Data and select What-If-Analysis.
Under What-If-Analysis, select Goal Seek
In set cell, select H6 (the formula)
The To value is considered as 66.45 (the value of the present value of annuity)
The H7 cell is selected for the 'by changing cell.'

Step 4:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 4

Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value

Step 5:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 5

The r value appears to be 18.6190266505771%

Hence, the r value is 18.62%

Compute the annual percentage rate:

APR=52(18.62%)=968.19%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of periods in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 968.19%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.1862)52−1=7,178.4521−1=7,177.4521

Hence, the effective annual rate is 7,177.4521 or 717,745.21%.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 6, Problem 77QP

a)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

a)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 390%, the effective annual rate is 4,197.74%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Compute the annual percentage rate:

APR=52(7.5%)=390%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 390%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.075)52−1=42.9774−1=41.9774

Hence, the effective annual rate is 0.41,9774 or 4,197.74%

b)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

b)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 421.62%, the effective annual rate is 5,662.75%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay back the full principal value. With the discount of 7.5%, Person X receives $9.25 for each $10 as the principal value. The weekly interest rates are calculated as follows:

$10=$9.25(1+r)r=($10$9.25)−1r=1.0811−1r=0.0811

Note: The dollar values that are used above are not relevant. In other words, it can also be written as $0.925 and $1 or $92.5 and $100 or in any other combination that provides similar rate of interest.

Hence, the r value is 0.0811 or 8.11%

Compute the annual percentage rate:

APR=52(8.11%)=421.62%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 421.62%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.0811)52−1=57.6275−1=56.6275

Hence, the effective annual rate is 56.6275 or 5,662.75%

c)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

c)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 968.19%, the effective annual rate is 717,745.21%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In this part, the present value of an annuity and the cash flow is given; with the help of the present value of annuity equation, the r value is found using a spreadsheet.

Formula to calculate the present value annuity:

Present value annuity=C{[1−(11+rt)]r}

Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. Using the formulae of the present value of annuity, the interest rate is computed using the spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$66.45=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 1

Type the formulae of the present value annuity in H6 in the spreadsheet and consider the r value as H7

Step 2:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 3

In the spreadsheet, go to Data and select What-If-Analysis.
Under What-If-Analysis, select Goal Seek
In set cell, select H6 (the formula)
The To value is considered as 66.45 (the value of the present value of annuity)
The H7 cell is selected for the 'by changing cell.'

Step 4:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 4

Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value

Step 5:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 5

The r value appears to be 18.6190266505771%

Hence, the r value is 18.62%

Compute the annual percentage rate:

APR=52(18.62%)=968.19%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of periods in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 968.19%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.1862)52−1=7,178.4521−1=7,177.4521

Hence, the effective annual rate is 7,177.4521 or 717,745.21%.

Answer 6

Chapter 6, Problem 77QP

a)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

a)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 390%, the effective annual rate is 4,197.74%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Compute the annual percentage rate:

APR=52(7.5%)=390%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 390%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.075)52−1=42.9774−1=41.9774

Hence, the effective annual rate is 0.41,9774 or 4,197.74%

Answer 7

Chapter 6, Problem 77QP

a)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

Answer 8

a)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 390%, the effective annual rate is 4,197.74%

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Compute the annual percentage rate:

APR=52(7.5%)=390%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 390%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.075)52−1=42.9774−1=41.9774

Hence, the effective annual rate is 0.41,9774 or 4,197.74%

Answer 13

b)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

b)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 421.62%, the effective annual rate is 5,662.75%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay back the full principal value. With the discount of 7.5%, Person X receives $9.25 for each $10 as the principal value. The weekly interest rates are calculated as follows:

$10=$9.25(1+r)r=($10$9.25)−1r=1.0811−1r=0.0811

Note: The dollar values that are used above are not relevant. In other words, it can also be written as $0.925 and $1 or $92.5 and $100 or in any other combination that provides similar rate of interest.

Hence, the r value is 0.0811 or 8.11%

Compute the annual percentage rate:

APR=52(8.11%)=421.62%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 421.62%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.0811)52−1=57.6275−1=56.6275

Hence, the effective annual rate is 56.6275 or 5,662.75%

Answer 14

b)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

Answer 15

b)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 421.62%, the effective annual rate is 5,662.75%

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay back the full principal value. With the discount of 7.5%, Person X receives $9.25 for each $10 as the principal value. The weekly interest rates are calculated as follows:

$10=$9.25(1+r)r=($10$9.25)−1r=1.0811−1r=0.0811

Note: The dollar values that are used above are not relevant. In other words, it can also be written as $0.925 and $1 or $92.5 and $100 or in any other combination that provides similar rate of interest.

Hence, the r value is 0.0811 or 8.11%

Compute the annual percentage rate:

APR=52(8.11%)=421.62%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of months in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 421.62%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.0811)52−1=57.6275−1=56.6275

Hence, the effective annual rate is 56.6275 or 5,662.75%

Answer 20

c)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

c)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 968.19%, the effective annual rate is 717,745.21%

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In this part, the present value of an annuity and the cash flow is given; with the help of the present value of annuity equation, the r value is found using a spreadsheet.

Formula to calculate the present value annuity:

Present value annuity=C{[1−(11+rt)]r}

Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. Using the formulae of the present value of annuity, the interest rate is computed using the spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$66.45=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 1

Type the formulae of the present value annuity in H6 in the spreadsheet and consider the r value as H7

Step 2:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 3

In the spreadsheet, go to Data and select What-If-Analysis.
Under What-If-Analysis, select Goal Seek
In set cell, select H6 (the formula)
The To value is considered as 66.45 (the value of the present value of annuity)
The H7 cell is selected for the 'by changing cell.'

Step 4:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 4

Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value

Step 5:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 5

The r value appears to be 18.6190266505771%

Hence, the r value is 18.62%

Compute the annual percentage rate:

APR=52(18.62%)=968.19%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of periods in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 968.19%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)

Compute the effective annual rate:

Effective annual rate=(1+(APR12)12−1)=(1+0.1862)52−1=7,178.4521−1=7,177.4521

Hence, the effective annual rate is 7,177.4521 or 717,745.21%.

Answer 21

c)

Summary Introduction

To calculate: The annual percentage rate and the effective annual rate

Introduction:

The annual rate that is earned from the investment or charged for a borrowing is an annual percentage rate and it is also represented as APR. Thus, the APR is calculated by multiplying the rate of interest for a year with the number of months in a year. The effective annual rate is the rate of interest that is expressed as if it were compounded once in a year.

Answer 22

c)

Expert Solution

Answer to Problem 77QP

The annual percentage rate is 968.19%, the effective annual rate is 717,745.21%

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake-up consumers. The store offers a week loan at the rate of interest of 7.5% per week. Then, after few days, the store again makes a one-week loan at a discount interest rate of 7.5% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 7.5% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $33.55. As this is a discount interest rate, the net proceeding of Person X will be $66.45. Thus, Person X has to pay $100 for a month and the store also lets Person X to pay $25 in installments for a week.

Explanation:

In this part, the present value of an annuity and the cash flow is given; with the help of the present value of annuity equation, the r value is found using a spreadsheet.

Formula to calculate the present value annuity:

Present value annuity=C{[1−(11+rt)]r}

Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. Using the formulae of the present value of annuity, the interest rate is computed using the spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$66.45=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 1

Type the formulae of the present value annuity in H6 in the spreadsheet and consider the r value as H7

Step 2:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 3

In the spreadsheet, go to Data and select What-If-Analysis.
Under What-If-Analysis, select Goal Seek
In set cell, select H6 (the formula)
The To value is considered as 66.45 (the value of the present value of annuity)
The H7 cell is selected for the 'by changing cell.'

Step 4:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 4

Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value

Step 5:

Fundamentals of Corporate Finance, Chapter 6, Problem 77QP , additional homework tip 5

The r value appears to be 18.6190266505771%

Hence, the r value is 18.62%

Compute the annual percentage rate:

APR=52(18.62%)=968.19%

Note: The annual percentage rate is computed by multiplying the interest rate with the number of periods in a year. Here, the interest is calculated per week and so the number of weeks in a year (52 weeks) is taken as the period.

Hence, the annual percentage rate is 968.19%

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)