Question

4. Quick Loans (a pay day loan company offers you “two for four or 1 knock on your door.” This means you get $2 today and have to repay $4 when you get your paycheck in one month (or else you get the “knock on your door,” which we can assume will be unpleasant). [Note: Large numbers are OK.] a. If you were brave enough to ask, what APR would the lender (Quick Loans) say you were paying? b. What is the effective annual return the lender (Quick Loans) earns on this lending business (the lender loans $2 today and gets $4 in one time period)?

Answer 1

a]

APR = monthly rate * number of months in a year

monthly rate = interest paid / amount borrowed

interest paid = amount repaid - amount borrowed = $4 - $2 = $2

monthly rate = $2 / $2 = 100%

APR = 100% * 12 = 1200%

b]

Effective annual return = (1 + monthly return)^{number of months in year} - 1

Effective annual return = (1 + 100%)¹² - 1

Effective annual return = 409500%