The Auto Loan Payment Formula: How to Calculate It Yourself

Components of the Loan Payment Formula

The monthly payment on any installment loan is determined by three key factors: the loan amount, the interest rate, and the loan term. The standard formula used for auto loans is:

Monthly Payment = L × [r(1 + r)^n] / [(1 + r)^n − 1], where L is the loan amount (the principal), r is the monthly interest rate (annual rate divided by 12), and n is the number of monthly payments (the term in months).

• Loan amount (L): The total amount borrowed, typically the vehicle price minus any down payment, trade-in value, and sometimes fees.
• Monthly interest rate (r): The annual percentage rate (APR) divided by 12. For example, a 9% APR becomes 0.09 ÷ 12 = 0.0075.
• Number of payments (n): The loan term in months. Common terms are 36, 48, 60, or 72 months.

Sources: Federal Reserve Board

Deriving the Monthly Interest Rate

Because the formula uses a monthly rate, you must convert the APR. Simply divide the APR by 12. For instance, if your APR is 9%, the monthly rate is 0.09 ÷ 12 = 0.0075. This monthly rate is used to calculate both the payment and the interest charged each month. The interest for a given month is the current outstanding balance multiplied by this monthly rate.

Sources: Federal Reserve Board

Step-by-Step Example

Let’s apply the formula to a concrete example from the Federal Reserve: a loan amount of $18,800, an APR of 9%, and a term of 48 months.

First, convert the APR to a monthly rate: 0.09 ÷ 12 = 0.0075. Next, compute (1 + r)^n: (1.0075)^48 ≈ 1.4322. Then plug the values into the formula:

• The first month's interest is the outstanding balance times the monthly rate: $18,800 × 0.0075 = $141.00.
• The principal portion of that payment is the total payment minus interest: $467.84 − $141.00 = $326.84.
• Each subsequent payment reduces the balance, and the interest portion decreases while the principal portion increases.

1. Monthly payment = 18,800 × [0.0075 × 1.4322] / [1.4322 − 1]
2. Simplify: 18,800 × 0.01074 / 0.4322
3. Monthly payment ≈ $467.84

Sources: Federal Reserve Board

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The loan amount (L) in the formula is the amount financed, not necessarily the full vehicle price. If you make a down payment or trade in a vehicle, that amount is subtracted from the price before financing.

Sources: Federal Reserve Board

Common Mistakes to Avoid

A frequent error is forgetting to convert the APR to a monthly rate. The formula expects the monthly rate, so using the annual rate will produce a payment that is far too high.

Another mistake is using the wrong loan amount. The loan amount must be the amount financed, not the sticker price. Always subtract your down payment.

Also, be aware that the loan term (n) must be in months. If you have a term in years, multiply by 12 before using the formula.

Using a Spreadsheet to Calculate Payments

If you prefer not to compute by hand, you can set up a simple spreadsheet. Most spreadsheet applications have a built-in function called PMT that does exactly this calculation.

In a cell, enter the PMT function with the monthly rate, the number of payments, and the loan amount. For example, =PMT(0.0075, 48, 18800) returns approximately -$467.84, because spreadsheet functions often return a negative value for a payment. To display a positive number, use = -PMT(0.0075, 48, 18800).

You can also create your own formula in a cell by typing the mathematical expression above. This allows you to adjust any variable and see how it affects the payment.