Question

Megan took out a loan of $85,600 at an interest rate of 11.5%, compounded monthly. She paid off the loan in full over the course of exactly twelve years. Assuming that Megan made the same payment every month for twelve years, what was her monthly payment?
a.
$1,125.03
b.
$629.52
c.
$1,098.52
d.
$820.33

Answer 1

Use the annuity (loan) payment formula:
Payment = P * i / (1 - (1+i)^(-n))
where P = 85,600, i = 0.115/12 ≈ 0.0095833333, n = 12*12 = 144.

Compute:
(1+i)^144 ≈ 3.9479, 1 - (1+i)^(-144) ≈ 0.7467,
Payment ≈ 85,600 * 0.0095833333 / 0.7467 ≈ $1,098.52.

Answer: c. $1,098.52