Compound Frequency 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 use the formula:

(1 + r/ m)^m - 1

Where:
r = the nominal annual interest rate (10%)
m = the number of compounding periods in a year (52 weeks divided by 2 weeks = 26)

Using this formula, we get:

(1 + 0.10 / 26)^26 - 1
= 1.109178 - 1
= 0.109178

To convert this to a percentage, we multiply by 100:

0.109178 x 100 = 10.9178%

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

Compound Frequency Payday Loans Are Very Short-Term Loans That Charge