The Pawn Shop loans money at an annual rate of 21 percent and compounds interest weekly. What is the actual rate being charged on these loans?

Question

Quizplus · Accepted Answer

To find the actual rate being charged on the loans, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual rate, n is the number of times compounded per year, and t is the time in years.

In this case, we have r = 21%, n = 52 (since interest is compounded weekly), and we want to find the value of r that makes A/P = 1 + r/n. Setting t = 1 year for simplicity, we get:

1 + r/n = (1 + 0.21/52)^52  (the left-hand side is the effective annual rate)

Solving for r, we get:

r ≈ 0.2332 or 23.32%

Therefore, the answer is B, 23.32 percent.

The Pawn Shop Loans Money at an Annual Rate of 21