c- The check-cashing store also makes one-month add-on interest loans at 8 percent discount interest per...

c- The check-cashing store also makes one-month add-on interest loans at 8 percent discount interest per week. Thus if you borrow $100 for one month (four weeks),the interest will be ($100 × 1.084 ) − 100 = $36.05. Because this is discount interest, your net loan proceeds today will be $63.95. You must then repay the store $100 at the end of the month. To help you out, though, the store lets you pay off this $100 in installments of $25 per week. What is the APR of this loan? What is the EAR? (Round your answers to 2 decimal places. (e.g., 32.16))

Solutions

Expert Solution

Net proceeds today = 63.95, Weekly installment = $25,

Total amount to be repaid = $100

No of weeks for which payment has to be made = Total amount to be repaid / Weekly installment = 100 / 25 = 4 weeks

We know that

APR = No of weeks in a year x weekly rate = 52 x weekly rate

We can find the weekly rate by using rate function in excel

Formula to be used in excel: =rate(nper,pmt,-pv)

Using rate function in excel, we get weekly rate of loan = 20.6327%

APR = Weekly rate x 52 = 52 x 20.6327% = 1072.9004% = 1072.90%

Hence Annual percentage rate = APR = 1072.90%

Effective annual rate = EAR = (1 + weekly rate)^{no of weeks
in a year} - 1 = (1 + 20.6327%)⁵² - 1 = (1.206327)⁵² - 1 = 17225.9234 - 1 = 17224.9234 = 1722492.34%

Hence EAR = 1722492.34%

jeff jeffy answered 8 months ago

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