Question

Suppose you can afford only $200 a month in car payments and your best loan option is a 60-month loan at 3%. How much money could you spend on a car?

That is, calculate the present value of the loan with these conditions.

Answer 1

$11,130.47

Explanation:

The amortization formula can be used. It tells you the monthly payment amount A for some principal P, interest rate r, and n payments.

A = P(r/12)/(1 -(1 +r/12)^(-n))

Filling in your values, we get ...

200 = P(.03/12)/(1 -(1 +.03/12)^-60) = P(.0025)/(1 -1.0025^-60)

P = 200(1 -1.0025^-60)/.0025 ≈ 200×55.6523577

P ≈ 11,130.47

The present value of the loan is $11,130.47.