Question

Sam is paying off his eight-year, $15,360 loan in semiannual installments. The loan has an interest rate of 9.58%, compounded semiannually, and a service charge of $1,294.64. Once the loan has been fully paid off, what percentage of the total finance charge will the service charge be? Round all dollar values to the nearest cent.
a.
5.48%
b.
8.43%
c.
18.55%
d.
15.65%

Answer 1

Periodic rate = 0.0958/2 = 0.0479, n = 8·2 = 16 periods.

Payment A = 15360·[0.0479/(1 − (1.0479)^−16)] ≈ $1,395.54 (rounded to nearest cent).

Total paid = 1,395.54·16 = $22,328.64.
Total finance charge = 22,328.64 − 15,360.00 = $6,968.64.

Service charge share = 1,294.64 / 6,968.64 ≈ 0.1855 = 18.55%.

Answer: c. 18.55%