suppose that you decide to buy a car for $60,000, including taxes and license fees. you saved $10,000 for a…

suppose that you decide to buy a car for $60,000, including taxes and license fees. you saved $10,000 for a down payment. the dealer is offering you a choice between two incentives. incentive a is $6000 off the price of the car, followed by a five - year loan at 6.85%. incentive b does not have a cash rebate, but provides free financing (no interest) over five years. what is the difference in monthly payments between the two offers? which incentive is the better deal? use pmt = p(r/n)/1-(1 + r/n)^(-nt). the difference in monthly payments between the two offers is $. (round to the nearest cent as needed.)

suppose that you decide to buy a car for $60,000, including taxes and license fees. you saved $10,000 for a down payment. the dealer is offering you a choice between two incentives. incentive a is $6000 off the price of the car, followed by a five - year loan at 6.85%. incentive b does not have a cash rebate, but provides free financing (no interest) over five years. what is the difference in monthly payments between the two offers? which incentive is the better deal? use pmt = p(r/n)/1-(1 + r/n)^(-nt). the difference in monthly payments between the two offers is $. (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Calculate the loan - amount for Incentive A

The price of the car is $60000$ and the down - payment is $10000$. With Incentive A, there is a $6000$ cash rebate. So the loan amount $P_A=(60000 - 10000-6000)=44000$. The annual interest rate $r = 6.85%=0.0685$, the number of times compounded per year $n = 12$ (monthly payments), and the number of years $t = 5$.

Step2: Calculate the monthly payment for Incentive A using the formula $PMT=\frac{P(\frac{r}{n})}{1-(1 + \frac{r}{n})^{-nt}}$

Substitute the values into the formula: [ \begin{align*} PMT_A&=\frac{44000\times(\frac{0.0685}{12})}{1-(1+\frac{0.0685}{12})^{-12\times5}}\ &=\frac{44000\times0.00570833}{1-(1 + 0.00570833)^{-60}}\ &=\frac{251.16652}{1 - 0.7049607}\ &=\frac{251.16652}{0.2950393}\ &\approx851.37 \end{align*} ]

Step3: Calculate the loan - amount for Incentive B

The price of the car is $60000$ and the down - payment is $10000$. So the loan amount $P_B=(60000 - 10000)=50000$. Since there is no interest ($r = 0$), the monthly payment $PMT_B=\frac{50000}{12\times5}=\frac{50000}{60}\approx833.33$.

Step4: Calculate the difference in monthly payments

The difference $\Delta PMT=|PMT_A - PMT_B|=|851.37-833.33| = 18.04$.

Answer:

$18.04$