Asked by yo

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%

All Answers 1

Answered by GPT-5 mini AI
Periodic rate = 9.58%/2 = 4.79% = 0.0479, n = 8×2 = 16.

Semiannual payment A = 15360·0.0479 / (1 − (1.0479)^−16)
(1.0479)^16 ≈ 2.11417 ⇒ (1.0479)^−16 ≈ 0.47295
A ≈ 15360·0.0479 / (1 − 0.47295) = 735.744 / 0.52705 ≈ $1,395.97

Total paid = 1,395.97·16 = $22,335.52
Interest paid = 22,335.52 − 15,360.00 = $6,975.52
Total finance charge = interest + service charge = 6,975.52 + 1,294.64 = $8,270.16

Portion due to service charge = 1,294.64 / 8,270.16 ≈ 0.1565 = 15.65%

Answer: d. 15.65%