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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.)

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Answer:

Following are the solution to this question:

Step-by-step explanation:

For incentive A

The car value = 57000

Calculating debt[tex]= 57000 - 10000[/tex]

                            [tex]= 47000[/tex]

Calculating the debt value after incentive [tex]= 47000 - 5000[/tex]

                                                                    [tex]= 42000[/tex]

[tex]PMT = \frac{P(\frac{r}{n})}{(1 - (1 + (\frac{r}{n}))^(-nt))}[/tex]

         [tex]= \frac{42000 \times (\frac{6.06 \%}{12})}{(1-(1+(\frac{6.06 \%}{12}))^{(-12 \times 4)})}[/tex]

         [tex]= \frac{42000 \times (0.00505)}{(1-(1+(0.00505))^{(-48)})}\\\\= \frac{212.1}{(1-(1+(0.00505))^{(-48)})}\\\\=\frac{212.1}{-1.74}\\\\= - 121.89 \ \ or \ \ 121.89[/tex]

For incentive  B

The car value = 57000

Calculating the debt value [tex]= 57000 - 10000[/tex]

                                            [tex]= 47000[/tex]

Calculating the monthly payment =[tex]\frac{47000}{(12*4)}[/tex]

                                                        [tex]= \frac{47000}{(48)}\\\\= \frac{47000}{(48)}\\\\=979.166[/tex]

difference:

[tex]=121.89 - 979.166\\\\ = - 854.276[/tex]

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