Question

ay you take out a loan with a principal of $44,500. The interest rate is 13.11%, compounded monthly. If you make consistent monthly payments and pay off the loan over the course of six and a half years, how much interest will you have paid in total? Round dollar amounts to the nearest cent.
a.
$21,849.92
b.
$3,018.03
c.
$20,003.60
d.
$24,321.18

Answer 1

Monthly rate r = 0.1311/12 = 0.010925. Number of months n = 6.5·12 = 78.

Monthly payment:
M = P·r / (1 − (1+r)^(−n))
= 44500(0.010925) / (1 − (1.010925)^(−78))
≈ $850.64 per month.

Total paid = 850.64 · 78 = $66,349.92.
Total interest = total paid − principal = 66,349.92 − 44,500.00 = $21,849.92.

Answer: a. $21,849.92