## Thinking Mathematically (6th Edition)

Published by Pearson

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

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 $\$50,000PMT = \frac{P}{nt}PMT = \frac{\$50,000}{(12)(5)}$ $PMT = \$833$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.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.