Question

Zoe paid off her loan with $4,924.80 after 40 months. The annual interest on the loan was 5.2%, with interest compounded monthly. She did not make any additional payments and was not charged any fees.

What was the initial amount of the loan?

(1 point)
$

Answer 1

Let P be the initial loan. With monthly compounding at 5.2% annual, the monthly rate is 0.052/12, so

P(1 + 0.052/12)^{40} = 4924.80.

Thus
P = 4924.80 / (1 + 0.052/12)^{40} ≈ 4924.80 / (1.0043333333)^{40} ≈ $4,142.60.