Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.6 Cars - Exercise Set 8.6: 9

Answer

The monthly payments with Incentive A are $\$65$ more than the monthly payments with Incentive B. Since there are 60 payments for each incentive, Incentive B requires less money to buy the car. Therefore, Incentive B is a better deal.

Work Step by Step

We can use this formula to calculate the payments for a loan: $PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$ $PMT$ is the amount of the regular payment $P$ is the amount of the loan $r$ is the interest rate $n$ is the number of payments per year $t$ is the number of years We can find the monthly payments for Incentive A. Since the down payment is $\$10,000$, and there is a $\$5000$ discount, the amount of the loan is $\$45,000$ $PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$ $PMT = \frac{(\$45,000)~(\frac{0.0734}{12})}{[1-(1+\frac{0.0734}{12})^{-(12)(5)}~]}$ $PMT = \$898$ The monthly payments with Incentive A are $\$898$ We can find the monthly payments for Incentive B. Since the down payment is $\$10,000$, the amount of the loan is $\$50,000$ $PMT = \frac{P}{nt}$ $PMT = \frac{\$50,000}{(12)(5)}$ $PMT = \$833$ The monthly payments with Incentive B are $\$833$ The monthly payments with Incentive A are $\$65$ more than the monthly payments with Incentive B. Since there are 60 payments for each incentive, Incentive B requires less money to buy the car. Therefore, Incentive B is a better deal.
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