Question

You go car shopping, knowing that you can afford monthly payments of $400. You also have a trade-in that you know is worth $3000. You intend to take a loan at an interest rate of 5% compounded monthly. If the payments last for 4 years, what is the most expensive car you can afford? Round your price to the nearest whole dollar.

Answer 1

$20,369

Explanation:

The annuity formula can tell you the present value P of a monthly payment A made n time at interest rate r per payment period.

P = A(1 -(1+r)^-n)/r

Here, we have A = 400, r = .05/12, n = 12*4 = 48, so the loan amount can be ...

P = 400(1 -(1+.05/12)^-48)/(.05/12) ≈ 17,369.18

Adding the value of the trade-in, we find we can afford a car priced at ...

$3000 + 17,369 = $20,369