Let’s take the example of Doris Rude, a taxi driver in Manhattan who got into a...

Let’s take the example of Doris Rude, a taxi driver in Manhattan who got into a borrowing trap with a payday-lender when she got behind on her medical bills[1]. For a fee of $30, the payday lender agreed to advance Doris a 2-week loan of $100. Doris wrote a check for $130 that the lender agreed to hold for 2 weeks. At the end of two weeks, however, with no change in her income or living expenses, Doris could not pay back the loan and the check bounced. She went to another lender to cover the debt of the first. Soon, she was bouncing from one payday lender to the other, six in all. Though cases like Doris’s have since generated increased scrutiny and regulation of the payday-loan industry, these usurious lenders still flourish and take advantage of borrowers who do not understand the power of compounding.

What was the 2-week interest rate on the initial loan?
Assuming Doris could not pay back any of the money that she borrowed (principal and fees/interest), and the lender continued to charge the same rate, how much money would Doris owe:
1. After 6 months?
2. After 1 year?

Expert Solution

a.

Loan Amount = $100

Period = 2 weeks

Fees = $30

Fees of $30 is same as the interest. Thus the interest rate for 2 weeks is $30/$100 = 30%

Thus, Annual Percentage Rate = 30%*(52/2) = 30%*26 = 780%

(Note: It is assumed that a year has 52 weeks. Since interest rate is for 2 weeks, 52 weeks is divided by 2)

b. how much money would Doris owe:

The question is silent on whether the interest is simple interest or compounding. Some pay-days loans have charged compounding interest as well. Have provided both the options below.

i. Amount owed after 6 month =

If interest rate is compounded : Loan Amount * (1+interest rate)^period = $100*(1+30%)^(26/2) = $100*30.28751=$3,028.75

If interest rate is not compounded but only a simple interest = Loan Amount * Interest rate *period = $100*30%*13 = $390

(1 year has 52 weeks and hence 6 months have 26 weeks. Since interest rate is for 2 weeks, interest will be paid for 13 periods (26/2))

ii. Amount owed after 1 year

If interest rate is compounded = Loan Amount * (1+interest rate)^period = $100*(1+30%)^(52/2) = $100*917.3333=$91,733.33

If interest rate is not compounded but only a simple interest = Loan Amount * Interest rate *period = $100*30%*26 = $780

(1 year has 52 weeks.Since interest rate is for 2 weeks, interest will be paid for 26 periods (52/2))

jeff jeffy answered 2 years ago

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