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.
