Question

Tamora just made the last of her monthly payments on her loan. She had been making these payments for the past nine years. The loan had a principal of $10,675 and an interest rate of 4.75%, compounded monthly. In addition, Tamora paid $939.25 in service charges. What was Tamora’s total finance charge? Round all dollar values to the nearest cent.

a.
$939.25
b.
$11,614.25
c.
$3,403.53
d.
$2,464.28

Answer 1

principal = 10,675
interest rate = 4.75% per year compounded monthly.
additional $939.25 was paid in service charges.

Annuity Payment PV
10,675 * (4.75%/12) ÷ [1 - (1+ 4.75%/12)^-12*9]
10,675 * 0.00396 ÷ [1 - (1.00396)^-108]
42.273 ÷ (1 - 0.655)
42.273 ÷ 0.345 = 122.53

122.53 * 108 = 13,233.24 interest and principal

13,233.24 + 939.25 - 10,675 = 3,497.49

The answer is closer to Choice C. The minimal difference in amount is due to the rounding off of decimal places.

Answer 2

Answer : $3403.53

Detailed Solution:
principal was 10,675
interest rate was 4.75% per year compounded annually.
additional $939.25 was paid in service charges.
payment on the principal plus interest is shown below:

pv = 10675
i = .0475/12 = .0039583333... per month.
n = 9 * 12 = 108 months.
fv = 0
pmt = 121.6635... per month
total finance charge would be (108 * 121.6635... + 939.25 - 10675).
that equals to 13139.66 + 939.25 - 10675 = 3403.91