Payday loans are very short-term loans that charge very high interest rates. You can borrow $550 today and repay $675 in two weeks. What is the compounded annual rate implied by this 22.73 percent rate charged for only two weeks?

Question

Quizplus · Accepted Answer

To find out the annual interest rate implied by the given two-week payday loan, we need to use the following formula:

A = P(1 + r/n)^(nt)

Where:
A = the total amount repaid
P = the principal amount borrowed
r = the annual interest rate
n = number of times the interest is compounded in a year
t = time period in years

Here, P = $550, A = $675, t = 2/52 years (since we're given the two-week rate), and n = 365 (since payday loans compound interest daily, even though you repay them weekly or biweekly).

Substituting these values in the formula, we get:

675 = 550(1 + r/365)^(365*2/52)

Solving for r, we get:

r = (365/14)[(675/550)^(14/365*2) - 1]

r = 20445.61 percent

Therefore, the answer is D) 20,445.61 percent.

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