Esther pays $532 per month for 6 years for a car. she made a down payment of $3,700. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?

Question

Mathematics

Mario Huff

24 November, 09:19

Esther pays $532 per month for 6 years for a car. she made a down payment of $3,700. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?

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Answers (1)

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Deacon · Answer 1

The amortization formula relates the principal and the loan payment by

A = Pi / (n (1 - (1 + r/n) ^ (-nt)))

You have

532 = P*0.071 / (12 * (1 - (1 +.071/12) ^ (-12*6))) = P*0.017097

P = 532/0.017097 = 31,116.45

This was the amount financed, so the original price is 3700 higher.

The cash price of the car was $31,116.45 + 3,700 = $34,816.45