Question

Brian took eight years to pay off his $71,900 loan. The loan had an interest rate of 8.16%, compounded quarterly. If Brian paid quarterly and made the same payment every time, how much was each payment that he made?
a.
$2,342.66
b.
$3,081.54
c.
$1,022.28
d.
$1,466.76

Answer 1

Quarterly rate i = 0.0816/4 = 0.0204. Number of quarters n = 8·4 = 32.

Payment = P · [i / (1 − (1 + i)^−n)]
= 71,900 · [0.0204 / (1 − (1.0204)^−32)]
≈ 71,900 · 0.042858673
≈ $3,081.54

Answer: b. $3,081.54