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

Question

Quizplus · Accepted Answer

To find the compound annual rate, we need to first calculate the effective annual interest rate for this loan. Using the formula:
Effective annual interest rate = (1 + periodic interest rate)^number of periods - 1

For this loan, the periodic interest rate is 10% for two weeks, which means there are 26 two-week periods in a year. Using the formula:
Effective annual interest rate = (1 + 0.1)^26 - 1 = 1.09178 or 109.178%

Therefore, the compound annual rate implied by this 10% rate charged for only two weeks is 1091.78%. Option C is the correct answer.

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