Question

Kurt has $4,500 for a down payment and thinks he can afford monthly payments of $300. If Kurt can finance a vehicle with a 7 percent, 4-year loan from the automobile dealer, what is the maximum amount he can afford to spend on the car? (Round off the answer to nearest units place.)

Answer 1

Ans. Kurt can purchase a car up to $17,080.40

Step-by-step explanation:

Hi, first we have to bring to present value this annuity of $300 per month, for that, we have to convert this effective annual rate of 7% to an effective monthly rate and finally, multiply by 12 the number of years in which Kurt plans to pay for the car, that is 48 months.

The rate is:

`r(monthly)=(1+r(annual))^{(1)/(12) } -1=(1+0.07)^{(1)/(12) } -1=0.00565415`

Or 0.565415% effective monthly.

Now it is time to use the following equation to find the present value of a $300 annuity. After that, we have to add the down payment and that is the price of the car.

`PresentValue=(A((1+r)^(n)-1) )/(r(1+r)^(n) )`

`PresentValue=(300((1+0.00565415)^(48)-1) )/(0.00565415(1+0.00565415)^(48) )`

`Present Value=12,580.40`

Now the car price has to be the present value that we just found plus the down payment that Kurt is planning to make.

`CarPrice=12,580.40+4,500=17,080.40`

Best of luck.