Question

Suppose that you decide to buy a car for ​$57,000​, 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 ​$5000 off the price of the​ car, followed by a four​-year loan at 6.06​%. Incentive B does not have a cash​ rebate, but provides free financing​ (no interest) over four years. What is the difference in monthly payments between the two​ offers? Which incentive is the better​ deal? Use PMT= P r n 1−1+ r n−nt. The difference in monthly payments between the two offers is ​$nothing. ​(Round to the nearest cent as​ needed.)

Answer 1

Following are the solution to this question:

Explanation:

For incentive A

The car value = 57000

Calculating debt
`= 57000 - 10000`

`= 47000`

Calculating the debt value after incentive
`= 47000 - 5000`

`= 42000`

`PMT = (P((r)/(n)))/((1 - (1 + ((r)/(n)))^(-nt)))`

`= (42000 * ((6.06 \%)/(12)))/((1-(1+((6.06 \%)/(12)))^((-12 * 4))))`

`= (42000 * (0.00505))/((1-(1+(0.00505))^((-48))))\\\\= (212.1)/((1-(1+(0.00505))^((-48))))\\\\=(212.1)/(-1.74)\\\\= - 121.89 \ \ or \ \ 121.89`

For incentive B

The car value = 57000

Calculating the debt value
`= 57000 - 10000`

`= 47000`

Calculating the monthly payment =
`(47000)/((12*4))`

`= (47000)/((48))\\\\= (47000)/((48))\\\\=979.166`

difference:

`=121.89 - 979.166\\\\ = - 854.276`