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%



Please select the best answer from the choices provided


A
B
C
D

Answer 1

Periodic rate = 9.58%/2 = 4.79% = 0.0479. Number of payments = 8*2 = 16.

Semiannual payment:
PMT = 15360 * [0.0479 / (1 - (1.0479)^-16)] ≈ $1,395.30.

Total paid = 1,395.30 * 16 = $22,324.80.
Total finance charge = total paid − principal = 22,324.80 − 15,360.00 = $6,964.80.

Service charge portion = 1,294.64 / 6,964.80 ≈ 0.1859 = 18.59% ≈ 18.55% (best match).

Answer: C