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

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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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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%.

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Students have asked these similar questions

Mf4. You've worked out a line of credit arrangement that allows you to borrow up to $80million at any time. The interest rate is0.61 percent per month. In addition, 4 percent of the amount that you borrow must be deposited in a non-interest-bearing account. Assume that your bank uses compound interest on its line of credit loans. Required: (a)What is the effective annual interest rate on this lending arrangement? (Do not round your intermediate calculations.) (b)Suppose you need $16 million today and you repay it in 6 months. How much interest will you pay? (Do not round your intermediate calculations.)

Question 5.A bank has borrowing needs at timeT >0. Show that by combining an FRAtrade today with a libor loan at timeT, the bank can today lock in its interest cost forthe periodTtoT+α. Does the borrowing bank need to buy or sell the FRA to do this?What is the fixed rate that the bank locks in?

Mf2. The treasurer of a small bank has borrowed funds for 3 months at an interest rate of 5.50% and has lent funds for 9 months at 6.50%. The total amount is USD25 million. To cover his exposure created by the mismatch of maturities, the dealer needs to borrow another USD25 million for 6 months, in 3 months’ time, and hedge the position now with an FRA. What is the treasurer’s break-even forward rate of interest, assuming no other costs?

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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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%.

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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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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%.

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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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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%.

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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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), Chapter 6, Problem 77QP , additional homework tip 2

Assume the r value as 0.10%

Step 3:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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:

FUND. OF CORPORATE FINANCE (LL), 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)