Question

You want to buy a new car, but you can make an initial payment of only $2,400 and can afford monthly payments of at most $500. 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?

Answer 1

Ans. The maximum price you can pay for the car is $21,387

Step-by-step explanation:

Hi, to find out what is the maximum price that you can pay, first we have to convert APR rate to an effective monthly rate, that is because you will make the payments in an monthly basis.

Therefore, the effective monthly rate of the credit is 12%/12 =1% effective monthly.

Now, let´s find out the maximum price of the car.

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

Where: A is the amount of money that you can pay every month; r is 1% effective rate; n is the periods of periodic payment.

So, everything should look like this:

`CarPrice=(500((1+0.01)^(48)-1) )/(0.01(1+0.01)^(48) ) +2,400= 21,387`

So, with a down payment of $2,400 and being able to pay $500 per month, the car that you can buy cannot have a price higher than $21,397.

Best of luck