How to Calculate Your Car Loan Payment by Hand

The Car Loan Payment Formula

Monthly car loan payments are computed using a standard amortization formula. The formula is: M = P × [i / (1 − (1 + i)^(−n))], where M is the monthly payment, P is the loan amount (principal), i is the monthly interest rate (annual rate divided by 12), and n is the number of monthly payments.

This formula accounts for the fact that each payment covers both interest and principal, and the balance decreases over time. Understanding this formula allows you to verify any quoted payment and see how changes in loan amount, interest rate, or term affect your payment.

• P = loan amount (also called principal)
• i = monthly interest rate (annual rate ÷ 12)
• n = total number of monthly payments

Sources: Certified AutoBrokers Inc.

Step 1: Determine Loan Amount (Price minus Down Payment)

The loan amount is what you actually borrow. It is the vehicle price plus taxes, fees, and any add-ons, minus your down payment, trade-in value, and any rebates.

A larger down payment directly reduces the loan amount, which lowers both your monthly payment and the total interest you pay over the life of the loan.

Sources: Consumer Financial Protection Bureau, Certified AutoBrokers Inc.

Step 2: Convert Annual Rate to Monthly Rate

The interest rate on a car loan is usually expressed as an annual percentage rate (APR). To use it in the payment formula, convert it to a monthly rate by dividing by 12.

Note that APR may include other costs, but for the purpose of the payment formula, you use the nominal annual rate (or the APR as a proxy). The difference between nominal rate and APR can matter for comparing offers, but the payment formula typically uses the stated annual rate.

Sources: Consumer Financial Protection Bureau, Certified AutoBrokers Inc.

Step 3: Calculate Monthly Payment Using the Formula

Now, let's plug the values into the formula. Using the example of a $30,000 loan at 5% APR for 60 months, the monthly rate i = 0.05 / 12 = 0.004167, and n = 60. The formula becomes: M = 30000 × [0.004167 / (1 − (1 + 0.004167)^(−60))].

Calculating the denominator: (1 + 0.004167)^(−60) ≈ 0.7792, so (1 − 0.7792) = 0.2208. Dividing 0.004167 by 0.2208 gives approximately 0.01887.

This payment includes both principal and interest. In the early months, a larger portion goes toward interest; later, more goes toward principal, a process known as amortization.

Sources: Certified AutoBrokers Inc.

Step 4: Include Taxes and Fees in the Calculation

Sales taxes and fees—such as document, title, and registration charges—can be either paid upfront or rolled into the loan amount. If you roll them in, your loan principal increases, raising your monthly payment. If you pay them upfront, your loan amount is lower.

To calculate accurately, add these costs to the vehicle price, then subtract any down payment and trade-in value. The result is the amount to finance.

Sources: Consumer Financial Protection Bureau, Calculator.net, Certified AutoBrokers Inc.

Example Scenarios: 36 vs. 60 vs. 72 Months

The loan term (number of months) significantly affects your monthly payment and total interest. A longer term reduces the monthly payment but increases the total interest paid over the life of the loan.

The table below, based on a $20,000 loan at 4.75% APR, illustrates this trade-off.

• A longer term can also increase the risk of owing more than the vehicle is worth.

Sources: Consumer Financial Protection Bureau

How to Use a Spreadsheet for the Calculation

Instead of doing the math by hand, you can use a spreadsheet function to compute the monthly payment. In Excel or Google Sheets, the PMT function does this: =PMT(rate, nper, -pv). For a $30,000 loan at 5% APR over 60 months, you would enter =PMT(0.05/12, 60, -30000), which returns approximately $565.77.

The negative sign for the present value (pv) is used to get a positive payment result. This is a convenient way to quickly test different loan amounts, rates, or terms.

Sources: Certified AutoBrokers Inc.