Buying a car often involves juggling the vehicle price, a trade-in, sales tax, and your down payment. Before you visit a dealership, calculating your expected auto loan payment gives you a number to negotiate from. It also makes it harder to be talked into a longer term just to hit a monthly payment target.
How the auto loan formula works
The calculator first works out what you actually borrow. Sales tax is charged on the price minus your trade-in; that tax is added to the price, and your down payment and trade-in are subtracted. The result is the amount financed.
That balance is then amortized like any fixed-rate loan, with r as the monthly rate (the APR divided by 12) and n as the number of months. Every payment is the same. Early payments are weighted toward interest, and as the balance falls, more of each payment goes to principal.
Worked example: financing a $35,000 vehicle
For example, suppose you buy a $35,000 car with a $5,000 down payment and a $2,000 trade-in. With a 6% sales tax rate, the tax on the remaining value is $1,980. This makes your total amount financed $29,980. On a standard 5-year loan at 7.2%, your monthly payment is $596.47. Over 60 months, you pay $5,808.38 in total interest, bringing the total cost of the car to $42,788.38.
If you stretch the loan to 72 months to lower the payment, your monthly bill drops to $514.01. However, the total interest climbs to $7,028.96. Extending it further to 84 months lowers the payment to $455.42 but raises the total interest to $8,274.88, significantly increasing the overall cost.
How to use the result
Use this estimate to establish your maximum budget before stepping onto the lot. Dealerships often negotiate based on the monthly payment, which can hide the true cost of a vehicle if they simply extend the loan term. Knowing exactly how the price, trade-in, and interest rate interact allows you to focus on the total amount financed rather than just the monthly figure. The same amortization math drives the personal loan calculator.
Limits and assumptions
This estimate assumes a fixed annual percentage rate and equal monthly payments. By default it calculates sales tax on the price after subtracting the trade-in credit, which is how most states handle it; if your state taxes the full price, switch the trade-in option and the tax is charged on the whole price instead. The calculator does not include dealer documentation fees, title and registration costs, extended warranties, or gap insurance. Always verify the final out-the-door price and terms with your lender or dealership. To budget for gas on top of the payment, use the fuel cost calculator.
Key terms
- Amount financed
- The actual loan balance after adding sales tax and subtracting your down payment and trade-in value.
- Trade-in
- The amount a dealership offers for your current vehicle, which is applied as a credit toward your new purchase.
- Down payment
- The cash amount you pay upfront, reducing the total amount you need to borrow.
- Sales tax
- A percentage tax imposed by your state and local government on the purchase of the vehicle.
- Loan term
- The duration of the auto loan, typically measured in months, such as 60 or 72 months.