Question

Nellie has a bankruptcy on her credit report and therefore pays higher interest rates on her current loans. She took out a car loan for $45,000 payable for 6 years at an interest rate of 15%. If she had not applied for bankruptcy, she would have been able to take out the loan at a rate of 6%. Approximately how much more in interest over the life of the loan does Nellie have to pay?
a.
$68,510.16
b.
$53,696.16
c.
$32,206.32
d.
$14,814.00

Answer 1

Use monthly payments. Principal P = $45,000, n = 6·12 = 72 months.

Monthly rate at 15%: r1 = 0.15/12 = 0.0125.
Monthly payment A1 = P·r1 / (1 − (1+r1)^−n).
Compute (1+r1)^72 ≈ 2.4459 so (1+r1)^−72 ≈ 0.40892.
A1 ≈ 45000·0.0125 / (1 − 0.40892) ≈ $951.39.
Total paid at 15% ≈ 951.39·72 ≈ $68,506.08 → interest ≈ 68,506.08 − 45,000 = $23,506.08.

Monthly rate at 6%: r2 = 0.06/12 = 0.005.
(1+r2)^72 ≈ 1.4322 so (1+r2)^−72 ≈ 0.6983.
A2 ≈ 45000·0.005 / (1 − 0.6983) ≈ $746.85.
Total paid at 6% ≈ 746.85·72 ≈ $53,692.20 → interest ≈ 53,692.20 − 45,000 = $8,692.20.

Extra interest paid ≈ 23,506.08 − 8,692.20 ≈ $14,813.88 ≈ $14,814.

Answer: d. $14,814.00.