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 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

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Answer 1

Question

Chapter 6, Problem 75QP

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 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 75QP

The annual percentage rate is 416% and the effective annual rate is 5,370.60%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Compute the annual percentage rate:

APR=52(8%)=416%

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

Hence, the annual percentage rate is 416%.

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+0.08)52−1=54.70604084−1=53.70604084

Hence, the effective annual rate is 0.53,70604084 or 5,370.60%.

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 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 75QP

The annual percentage rate is 451.88% and the effective annual rate is 7,518.31%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay the full principal value back. Person X receives $9.2 for each $10 as the principal value, with the discount of 8%. The weekly interest rates are calculated as follows:

$10=$9.2(1+r)r=($10$9.2)−1r=1.086956522−1r=0.086956522

Note: The dollar values that are used above are not relevant. In other words,it can also be written as $0.92 and $1, or $92 and $100, or in any other combination that provides a similar rate of interest.

Hence, the r value is 0.0869 or 8.69%.

Compute the annual percentage rate:

APR=52(8.69%)=451.88%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 451.88%.

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+0.0869)52−1=76.18309552−1=75.18309552

Hence, the effective annual rate is 75.18309552 or 7,518.31%

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 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 75QP

The annual percentage rate is 1,072.76%and the effective annual rate is 17,204.88622%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In this part, the present value of anannuity 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 formula of the present value of annuity, the interest rate is computed throughthe spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$63.95=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 1

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

Step 2:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 2

Assume the r value as 0.10%.

Step 3:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 3

In the spreadsheet, go to Dataand select What-If-Analysis.
UnderWhat-If-Analysis,select Goal Seek.
In set cell, select H6 (the formula).
The To value is considered as 63.95 (the value of the present value of annuity).
The H7 cell is selected for the by changing cell.

Step 4:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , 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 Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 5

The r value appears to be 20.6326657269649%.

Hence, the r value is 20.63%.

Compute the annual percentage rate:

APR=52(20.63%)=1,072.76%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 1,072.76%.

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+0.2063)52−1=17,205.88622−1=17,204.88622

Hence, the effective annual rate is 17,204.88622%.

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Students have asked these similar questions

Pam and Jim are saving money for their two children who they plan to send to university.The eldest child will enter university in 5 years while the younger will enter in 7 years. Each child is expected spend four years at university. University fees are currently R20 000 per year and are expected to grow at 5% per year. These fees are paid at the beginning of each year.Pam and Jim currently have R40 000 in their savings and their plan is to save a fixed amount each year for the next 5 years. The first deposit taking place at the end of the current year and the last deposit at the date the first university fees are paid.Pam and Jim expect to earn 10% per year on their investments.What amount should they invest each year to meet the cost of their children’s university fees?

You make a loan of R100 000, with annual payments being made at the end of each year for the next 5 years at a 10% interest rate. How much interest is paid in the second year?

Answer 2

Question

Chapter 6, Problem 75QP

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 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 75QP

The annual percentage rate is 416% and the effective annual rate is 5,370.60%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Compute the annual percentage rate:

APR=52(8%)=416%

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

Hence, the annual percentage rate is 416%.

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+0.08)52−1=54.70604084−1=53.70604084

Hence, the effective annual rate is 0.53,70604084 or 5,370.60%.

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 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 75QP

The annual percentage rate is 451.88% and the effective annual rate is 7,518.31%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay the full principal value back. Person X receives $9.2 for each $10 as the principal value, with the discount of 8%. The weekly interest rates are calculated as follows:

$10=$9.2(1+r)r=($10$9.2)−1r=1.086956522−1r=0.086956522

Note: The dollar values that are used above are not relevant. In other words,it can also be written as $0.92 and $1, or $92 and $100, or in any other combination that provides a similar rate of interest.

Hence, the r value is 0.0869 or 8.69%.

Compute the annual percentage rate:

APR=52(8.69%)=451.88%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 451.88%.

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+0.0869)52−1=76.18309552−1=75.18309552

Hence, the effective annual rate is 75.18309552 or 7,518.31%

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 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 75QP

The annual percentage rate is 1,072.76%and the effective annual rate is 17,204.88622%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In this part, the present value of anannuity 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 formula of the present value of annuity, the interest rate is computed throughthe spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$63.95=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 1

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

Step 2:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 2

Assume the r value as 0.10%.

Step 3:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 3

In the spreadsheet, go to Dataand select What-If-Analysis.
UnderWhat-If-Analysis,select Goal Seek.
In set cell, select H6 (the formula).
The To value is considered as 63.95 (the value of the present value of annuity).
The H7 cell is selected for the by changing cell.

Step 4:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , 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 Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 5

The r value appears to be 20.6326657269649%.

Hence, the r value is 20.63%.

Compute the annual percentage rate:

APR=52(20.63%)=1,072.76%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 1,072.76%.

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+0.2063)52−1=17,205.88622−1=17,204.88622

Hence, the effective annual rate is 17,204.88622%.

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Answer 3

Question

Chapter 6, Problem 75QP

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 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 75QP

The annual percentage rate is 416% and the effective annual rate is 5,370.60%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Compute the annual percentage rate:

APR=52(8%)=416%

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

Hence, the annual percentage rate is 416%.

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+0.08)52−1=54.70604084−1=53.70604084

Hence, the effective annual rate is 0.53,70604084 or 5,370.60%.

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 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 75QP

The annual percentage rate is 451.88% and the effective annual rate is 7,518.31%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay the full principal value back. Person X receives $9.2 for each $10 as the principal value, with the discount of 8%. The weekly interest rates are calculated as follows:

$10=$9.2(1+r)r=($10$9.2)−1r=1.086956522−1r=0.086956522

Note: The dollar values that are used above are not relevant. In other words,it can also be written as $0.92 and $1, or $92 and $100, or in any other combination that provides a similar rate of interest.

Hence, the r value is 0.0869 or 8.69%.

Compute the annual percentage rate:

APR=52(8.69%)=451.88%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 451.88%.

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+0.0869)52−1=76.18309552−1=75.18309552

Hence, the effective annual rate is 75.18309552 or 7,518.31%

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 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 75QP

The annual percentage rate is 1,072.76%and the effective annual rate is 17,204.88622%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In this part, the present value of anannuity 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 formula of the present value of annuity, the interest rate is computed throughthe spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$63.95=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 1

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

Step 2:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 2

Assume the r value as 0.10%.

Step 3:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 3

In the spreadsheet, go to Dataand select What-If-Analysis.
UnderWhat-If-Analysis,select Goal Seek.
In set cell, select H6 (the formula).
The To value is considered as 63.95 (the value of the present value of annuity).
The H7 cell is selected for the by changing cell.

Step 4:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , 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 Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 5

The r value appears to be 20.6326657269649%.

Hence, the r value is 20.63%.

Compute the annual percentage rate:

APR=52(20.63%)=1,072.76%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 1,072.76%.

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+0.2063)52−1=17,205.88622−1=17,204.88622

Hence, the effective annual rate is 17,204.88622%.

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Answer 4

Question

Chapter 6, Problem 75QP

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 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 75QP

The annual percentage rate is 416% and the effective annual rate is 5,370.60%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Compute the annual percentage rate:

APR=52(8%)=416%

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

Hence, the annual percentage rate is 416%.

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+0.08)52−1=54.70604084−1=53.70604084

Hence, the effective annual rate is 0.53,70604084 or 5,370.60%.

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 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 75QP

The annual percentage rate is 451.88% and the effective annual rate is 7,518.31%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay the full principal value back. Person X receives $9.2 for each $10 as the principal value, with the discount of 8%. The weekly interest rates are calculated as follows:

$10=$9.2(1+r)r=($10$9.2)−1r=1.086956522−1r=0.086956522

Note: The dollar values that are used above are not relevant. In other words,it can also be written as $0.92 and $1, or $92 and $100, or in any other combination that provides a similar rate of interest.

Hence, the r value is 0.0869 or 8.69%.

Compute the annual percentage rate:

APR=52(8.69%)=451.88%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 451.88%.

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+0.0869)52−1=76.18309552−1=75.18309552

Hence, the effective annual rate is 75.18309552 or 7,518.31%

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 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 75QP

The annual percentage rate is 1,072.76%and the effective annual rate is 17,204.88622%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In this part, the present value of anannuity 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 formula of the present value of annuity, the interest rate is computed throughthe spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$63.95=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 1

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

Step 2:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 2

Assume the r value as 0.10%.

Step 3:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 3

In the spreadsheet, go to Dataand select What-If-Analysis.
UnderWhat-If-Analysis,select Goal Seek.
In set cell, select H6 (the formula).
The To value is considered as 63.95 (the value of the present value of annuity).
The H7 cell is selected for the by changing cell.

Step 4:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , 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 Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 5

The r value appears to be 20.6326657269649%.

Hence, the r value is 20.63%.

Compute the annual percentage rate:

APR=52(20.63%)=1,072.76%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 1,072.76%.

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+0.2063)52−1=17,205.88622−1=17,204.88622

Hence, the effective annual rate is 17,204.88622%.

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Answer 5

Chapter 6, Problem 75QP

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 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 75QP

The annual percentage rate is 416% and the effective annual rate is 5,370.60%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Compute the annual percentage rate:

APR=52(8%)=416%

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

Hence, the annual percentage rate is 416%.

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+0.08)52−1=54.70604084−1=53.70604084

Hence, the effective annual rate is 0.53,70604084 or 5,370.60%.

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 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 75QP

The annual percentage rate is 451.88% and the effective annual rate is 7,518.31%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay the full principal value back. Person X receives $9.2 for each $10 as the principal value, with the discount of 8%. The weekly interest rates are calculated as follows:

$10=$9.2(1+r)r=($10$9.2)−1r=1.086956522−1r=0.086956522

Note: The dollar values that are used above are not relevant. In other words,it can also be written as $0.92 and $1, or $92 and $100, or in any other combination that provides a similar rate of interest.

Hence, the r value is 0.0869 or 8.69%.

Compute the annual percentage rate:

APR=52(8.69%)=451.88%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 451.88%.

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+0.0869)52−1=76.18309552−1=75.18309552

Hence, the effective annual rate is 75.18309552 or 7,518.31%

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 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 75QP

The annual percentage rate is 1,072.76%and the effective annual rate is 17,204.88622%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In this part, the present value of anannuity 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 formula of the present value of annuity, the interest rate is computed throughthe spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$63.95=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 1

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

Step 2:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 2

Assume the r value as 0.10%.

Step 3:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 3

In the spreadsheet, go to Dataand select What-If-Analysis.
UnderWhat-If-Analysis,select Goal Seek.
In set cell, select H6 (the formula).
The To value is considered as 63.95 (the value of the present value of annuity).
The H7 cell is selected for the by changing cell.

Step 4:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , 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 Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 5

The r value appears to be 20.6326657269649%.

Hence, the r value is 20.63%.

Compute the annual percentage rate:

APR=52(20.63%)=1,072.76%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 1,072.76%.

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+0.2063)52−1=17,205.88622−1=17,204.88622

Hence, the effective annual rate is 17,204.88622%.

Answer 6

Chapter 6, Problem 75QP

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 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 75QP

The annual percentage rate is 416% and the effective annual rate is 5,370.60%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Compute the annual percentage rate:

APR=52(8%)=416%

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

Hence, the annual percentage rate is 416%.

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+0.08)52−1=54.70604084−1=53.70604084

Hence, the effective annual rate is 0.53,70604084 or 5,370.60%.

Answer 7

Chapter 6, Problem 75QP

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 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 75QP

The annual percentage rate is 416% and the effective annual rate is 5,370.60%.

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 consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Compute the annual percentage rate:

APR=52(8%)=416%

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

Hence, the annual percentage rate is 416%.

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+0.08)52−1=54.70604084−1=53.70604084

Hence, the effective annual rate is 0.53,70604084 or 5,370.60%.

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 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 75QP

The annual percentage rate is 451.88% and the effective annual rate is 7,518.31%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay the full principal value back. Person X receives $9.2 for each $10 as the principal value, with the discount of 8%. The weekly interest rates are calculated as follows:

$10=$9.2(1+r)r=($10$9.2)−1r=1.086956522−1r=0.086956522

Note: The dollar values that are used above are not relevant. In other words,it can also be written as $0.92 and $1, or $92 and $100, or in any other combination that provides a similar rate of interest.

Hence, the r value is 0.0869 or 8.69%.

Compute the annual percentage rate:

APR=52(8.69%)=451.88%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 451.88%.

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+0.0869)52−1=76.18309552−1=75.18309552

Hence, the effective annual rate is 75.18309552 or 7,518.31%

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 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 75QP

The annual percentage rate is 451.88% and the effective annual rate is 7,518.31%.

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 consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In the discount loan, the amount that Person X gets is reduced by the discount and Person X has to pay the full principal value back. Person X receives $9.2 for each $10 as the principal value, with the discount of 8%. The weekly interest rates are calculated as follows:

$10=$9.2(1+r)r=($10$9.2)−1r=1.086956522−1r=0.086956522

Note: The dollar values that are used above are not relevant. In other words,it can also be written as $0.92 and $1, or $92 and $100, or in any other combination that provides a similar rate of interest.

Hence, the r value is 0.0869 or 8.69%.

Compute the annual percentage rate:

APR=52(8.69%)=451.88%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 451.88%.

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+0.0869)52−1=76.18309552−1=75.18309552

Hence, the effective annual rate is 75.18309552 or 7,518.31%

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 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 75QP

The annual percentage rate is 1,072.76%and the effective annual rate is 17,204.88622%.

Explanation of Solution

Given information:

A check-cashing store makes a personal loan to wake consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In this part, the present value of anannuity 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 formula of the present value of annuity, the interest rate is computed throughthe spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$63.95=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 1

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

Step 2:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 2

Assume the r value as 0.10%.

Step 3:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 3

In the spreadsheet, go to Dataand select What-If-Analysis.
UnderWhat-If-Analysis,select Goal Seek.
In set cell, select H6 (the formula).
The To value is considered as 63.95 (the value of the present value of annuity).
The H7 cell is selected for the by changing cell.

Step 4:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , 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 Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 5

The r value appears to be 20.6326657269649%.

Hence, the r value is 20.63%.

Compute the annual percentage rate:

APR=52(20.63%)=1,072.76%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 1,072.76%.

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+0.2063)52−1=17,205.88622−1=17,204.88622

Hence, the effective annual rate is 17,204.88622%.

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 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 75QP

The annual percentage rate is 1,072.76%and the effective annual rate is 17,204.88622%.

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 consumers up. The store offers a week loan at the rate of interest of 8% per week. Then, after a few days, the store makes a one-week loan again at a discount interest rate of 8% for a week. The store also makes an add-on interest on the loan at a discount interest rate of 8% for a week.

Thus, if Person X borrows $100 for 4 weeks, the interest would be $36.05. As this is a discount interest rate, the net proceeding of Person X will be $63.95. Thus, Person X has to pay $100 for a month and the store lets Person X to pay $25 in installments fora week.

Explanation:

In this part, the present value of anannuity 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 formula of the present value of annuity, the interest rate is computed throughthe spreadsheet method.

Compute the present value annuity:

Present value annuity=C{[1−(1(1+r)t)]r}$63.95=$25{[1−(1(1+r)4)]r}

Compute the interest rate using the spreadsheet:

Step 1:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 1

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

Step 2:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 2

Assume the r value as 0.10%.

Step 3:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 3

In the spreadsheet, go to Dataand select What-If-Analysis.
UnderWhat-If-Analysis,select Goal Seek.
In set cell, select H6 (the formula).
The To value is considered as 63.95 (the value of the present value of annuity).
The H7 cell is selected for the by changing cell.

Step 4:

Fundamentals of Corporate Finance Alternate Edition, Chapter 6, Problem 75QP , 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 Alternate Edition, Chapter 6, Problem 75QP , additional homework tip 5

The r value appears to be 20.6326657269649%.

Hence, the r value is 20.63%.

Compute the annual percentage rate:

APR=52(20.63%)=1,072.76%

Note: The annual percentage rate is computed by multiplying the interest rate withthe 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 1,072.76%.

Formula to calculate the effective annual rate:

Effective annual rate=(1+(APR12)12−1)