Question

Roderigo has just finished paying back his $8,575 unsubsidized Stafford loan, which he took out to fund his four-year degree. The loan had a duration of ten years and an interest rate of 7.1%, compounded monthly. Roderigo will allow interest capitalization. If Roderigo made monthly payments to pay off his loan, how much interest did he pay in total? Round all dollar values to the nearest cent.
a.
$4,547.02
b.
$3,426.20
c.
$7,353.80
d.
$5,436.20



Please select the best answer from the choices provided


A
B
C
D

Answer 1

First compute the monthly interest rate and number of payments:
- i = 0.071/12 = 0.005916666666666667
- n = 10·12 = 120

Monthly payment M is
M = P·i / (1 − (1 + i)^{−n})
= 8575·0.005916666666666667 / (1 − (1.0059166666666667)^{−120})
≈ $100.01 (rounded)

Total paid = 120·M ≈ $12,001.20
Total interest = total paid − principal ≈ 12,001.20 − 8,575.00 = $3,426.20

Answer: B.