Payday loans are very short-term loans that charge very high interest rates. You can borrow $500 today and repay $550 in ten weeks. What is the compound annual rate implied by this 10 percent rate charged for only ten weeks?

Question

Quizplus · Accepted Answer

The compound annual rate (CAR) can be calculated using the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the amount on maturity, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time the money is borrowed for in years. In this case, we're looking for r, the annual interest rate, given that $500 grows to $550 in 10 weeks (which is 10/52 years since there are 52 weeks in a year). The interest rate for 10 weeks is 10%, but we need to find the equivalent annual rate if that rate were compounded weekly for a year. The correct calculation involves finding the rate that would lead to the same growth over a year as the 10% does over 10 weeks, compounded weekly. The correct answer, 64.15%, reflects the annualized interest rate, taking into account the effect of compounding over the course of a year.

Payday Loans Are Very Short-Term Loans That Charge Very High