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 know how many times the interest is compounded in a year. As the loan term is only two weeks, we can assume that the interest is compounded every two weeks.

Using the formula for compound interest, we can calculate the effective annual rate as:

(1 + r/n)^n - 1 = 0.1

where r is the annual rate and n is the number of compounding periods per year.

Substituting n = 26 (to represent 52 weeks in a year divided into 2-week periods) and solving for r, we get:

r = (1 + 0.1/26)^26 - 1 = 10.9178 or 1091.78%

Therefore, the compound annual rate implied by this loan is 1091.78%, which is closest to option C.

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