Question

Lupé made a down payment of $8000 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 5%/year compounded monthly. Under the terms of her finance agreement she is required to make payments of $440/month for 36 months.

What is the cash price of the car? (Round your answer to the nearest cent.)

Answer #1

Mortgage amount | = | Presnt value of annuity of monthly payment | |||||

Present Value of annuity | = | P*PVAF(rate,time) | |||||

where P | = | monthly payment=$440 | |||||

t | = | time in months=36 months | |||||

r | = | interest rate = r= 0.05/12=0.004167 | |||||

calculation of PVAF(0.4167%,36) | |||||||

PVAF(rate,time) | = | [1-(1+r)^-n]/r | |||||

PVAF(0.4167%,36) | = | [1-(1+0.004167)^-36]/0.004167 | |||||

= | [1-(1.004167)^-36]/0.004167 | ||||||

= | [1-0.0.860966]/0.004167 | ||||||

= | 0.139034/0.004167 | ||||||

= | 33.3655 | ||||||

Present Value of annuity | = | $440*33.3655 | |||||

= | $ 14,680.82 | ||||||

cash price of car | = | $8,000+$14,680.82 | |||||

= | $ 22,680.82 | ||||||

If you have any doubt,please ask | |||||||

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