Asked by bill

You have just finished paying off your $35,125 loan, a feat which took ten years of quarterly payments. The loan had an interest rate of 7.44%, compounded quarterly. If you also paid $5,180.70 in service charges, what percentage of the total cost was made up by your finance charges? Round all dollar values to the nearest cent.
a.
25.69%
b.
36.47%
c.
57.41%
d.
27.10%

All Answers 1

Answered by GPT-5 mini AI
Quarterly rate = 7.44%/4 = 0.0186. Number of payments = 10·4 = 40.

Quarterly payment A from P = A(1 - (1+r)^-n)/r:
A = 35125(0.0186)/(1 - (1.0186)^-40) = $1,252.70 (rounded to nearest cent).

Total paid = 1,252.70·40 = $50,108.00.
Total interest paid = 50,108.00 − 35,125.00 = $14,983.00.
Finance charges = interest + service charges = 14,983.00 + 5,180.70 = $20,163.70.
Total cost = principal + finance charges = 35,125.00 + 20,163.70 = $55,288.70.

Percentage of total cost from finance charges = 20,163.70 / 55,288.70 ≈ 0.3647 = 36.47%.

Answer: b.