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%

Question

Business

Misael

29 October, 10:52

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%

+2

Answers (1)

Know the Answer?

Christopher · Answer 1

We are given with

P = $15,360

n = 8 years or 16 semi-annuals

r = 9.58% compounded semiannually

S = 1294.64

The future amount of the loan is

F = P (1 + i) ^n

i should be the effective interest rate of r

n should be the number of payments

F = 15360 (1 + 9.58/2) ^16

Solve for F and divide by the service charge to the answer