
Concept explainers
a)
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)

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:
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:
Compute the effective annual rate:
Hence, the effective annual rate is 0.41,9774 or 4,197.74%
b)
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)

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:
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:
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:
Compute the effective annual rate:
Hence, the effective annual rate is 56.6275 or 5,662.75%
c)
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)

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
Formula to calculate the present value annuity:
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:
Compute the interest rate using the spreadsheet:
Step 1:
- Type the formulae of the present value annuity in H6 in the spreadsheet and consider the r value as H7
Step 2:
- Assume the r value as 0.10%
Step 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:
- Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value
Step 5:
- The r value appears to be 18.6190266505771%
Hence, the r value is 18.62%
Compute the annual percentage rate:
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:
Compute the effective annual rate:
Hence, the effective annual rate is 7,177.4521 or 717,745.21%.
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