Question

You want to buy a new car, but you can make an initial payment of only $2,000 and can afford monthly payments of at most $400. a. If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the maximum price you can pay for the car? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

Ans. The maximum price that you can pay for a car is $17,189.58

Explanation:

Hi, since the payments are going to be made every month, for 48 months at a 12% APR, all we need to do is convert this nominal fixed rate into an effective rate, that is by dividing by 12. It means that the rate of the loan is 1% effective monthly. With that in mind, let´s work on the following formula.

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

Everything should look like this

$PresentValue=\frac{400((1+0.01)^{48}-1) }{0.01(1+0.01)^{n} }$

$PresentValue=400(37.9739595)$

$Present Value=15,189.58$

Now, let´s not forget that you actually have $2,000 cash more to buy the car, therefore, the car that you can buy, paying 400/month, at a 12% APR for 48 months can´t cost more than $17,189.58.

Best of luck