Question

Sarah recently purchased her first car for $18,500. She put 10% down and financed the remaining 90% of the purchase price over 48 months at 1.9% APR compounded monthly.

If Sarah keeps her car for the duration of the loan, find the total amount that Sarah paid for her car to the nearest cent.

Answer 1

Down payment = 10% of 18,500 = 1,850

Amount borrowed = 90% of 18,500

Amount borrowed = 16,650

Monthly rate = 1.9% / 12 = 0.158333%

Present value = Monthly payments * [1 - 1 / (1 + r)^n] / r

16,650 = Monthly payments * [1 - 1 / (1 + 0.00158333)^48] / 0.00158333

16,650 = Monthly payments * [1 - 0.926872] / 0.00158333

16,650 = Monthly payments * 46.186164

Monthly payments = 360.498

Total amount paid = (360.498 * 48) + 1,850

Total amount paid = $19,153.90