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 : $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

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.