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

Answer:

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

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:

$r(monthly)=(1+r(annual))^{\frac{1}{12} } -1=(1+0.07)^{\frac{1}{12} } -1=0.00565415$

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.

$PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

$PresentValue=\frac{300((1+0.00565415)^{48}-1) }{0.00565415(1+0.00565415)^{48} }$

$Present Value=12,580.40$

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.