Compound Frequency Payday loans are very short-term loans that charge very high interest rates. You can borrow $600 today and repay $675 in two weeks. What is the compound annual rate implied by this 12.5 percent rate charged for only two weeks?

Question

Quizplus · Accepted Answer

To find the compound annual rate, we need to use the formula:

(1 + i)^n = (A/P)

Where i is the annual interest rate, n is the number of compounding periods per year, A is the final amount, and P is the initial principal.

Plugging in the given values, we get:

(1 + i/26)^26 = 675/600

Simplifying, we get:

(1 + i/26)^26 = 1.125

Taking the 26th root of both sides, we get:

1 + i/26 = 1.125^(1/26)

Solving for i, we get:

i = (1.125^(1/26) - 1) * 26

i ≈ 2037.71%

Therefore, the compound annual rate implied by this payday loan is 2037.71%, which corresponds to answer choice C.

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