Sarah recently purchased her first car for $18,500. She put 10% down and financed the remaining...

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.

Solutions

Expert Solution

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

jeff jeffy answered 2 years ago

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