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 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 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:
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:
Compute the effective annual rate:
Hence, the effective annual rate is 0.53,70604084 or 5,370.60%.
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 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 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:
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:
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:
Compute the effective annual rate:
Hence, the effective annual rate is 75.18309552 or 7,518.31%
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 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 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
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 formula of the present value of annuity, the interest rate is computed throughthe spreadsheet method.
Compute the present value annuity:
Compute the interest rate using the spreadsheet:
Step 1:
- Type the formula 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 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:
- 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 20.6326657269649%.
Hence, the r value is 20.63%.
Compute the annual percentage rate:
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:
Compute the effective annual rate:
Hence, the effective annual rate is 17,204.88622%.
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Chapter 6 Solutions
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