How to Compute Monthly Auto Loan Payments

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When you take out an auto loan, there are several factors that determine your monthly car loan payments: amount of money borrowed (called the 'principal'), number of months in the loan period, and the annual interest rate. the more you borrow and the higher the interest rate, the higher your monthly payments will be.

A shorter loan period will also mean higher payments each month, but the shorter the loan period, the less interest you pay.

If you are curious about how monthly auto loan payments are calculated, the steps below will show you how to do it. This can help you when making a budget, or negotiating a car deal.

Things You Will Need

Scientific Calculator

Step 1

Assign names to the variables in calculating monthly payments. Call the principal P, call the number of months n and call the annual interest rate r. (r in decimal form, e.g., 7% = .07)

When you compute monthly payments, you also need to know the monthly interest rate, which is r/12. We will use i for monthly interest rate.

Step 2

Now, plug P, n, and i into this formula:

Monthly payment = [Pi(1+i)ⁿ]/[(1+i)ⁿ - 1]

The little superscript ⁿ is an exponent.

See image for a larger view of the formula.

Step 3

Use the equation to test different values of P, n, and i to see how your monthly payments change. By playing around with different numbers, you can discover the loan terms that fit your monthly budget. Some examples are discussed below.

Suppose that the loan amount is $12,000, the annual interest rate is 6% and the loan period is 36 months. Then,

P = 12000
n = 36
i = .06/12 = .005

So the monthly payments are

[(12000)(.005)(1.005)³⁶]/[(1.005)³⁶ - 1]
= [(60)(1.19668)]/[1.19668 - 1]
= [71.8008]/[.19668]
= 365.06

So for these car loan terms, the monthly payments come out to be $365.06 each month.

If you multiply $365.06 by 36 months, you get $13,142.16. This is the total amount you will pay by the end of 3 years. Notice that $13,142 - $12,000 = $1,142. That means you pay $1,142 in interest charges.

Another Example

Suppose that the amount of the loan is $15,000, the annual interest rate is 9%, and the length of the auto loan period is 48 months. Then P = 15000, i = .0075, and n = 48. If we plug those numbers into the formula, we get $373.28 for the monthly payments.

Since $373.28 times 48 equals $17,917, the total amount of interest paid is $2,917.