Auto Loan Calculator Formula
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Reviewed by Calculator Editorial Team
An auto loan calculator helps you determine your monthly payments, total interest paid, and loan payoff date based on the loan amount, interest rate, and term. This guide explains the auto loan formula, how to use the calculator, and what the results mean.
How to Use This Calculator
To calculate your auto loan payments:
- Enter the loan amount (principal) in dollars.
- Enter the annual interest rate (APR).
- Select the loan term in years.
- Click "Calculate" to see your monthly payment and other details.
The calculator uses the standard auto loan formula to compute your payment. You can also view a breakdown of your loan payments over time with the included chart.
Auto Loan Formula
The auto loan payment is calculated using the standard loan payment formula:
Monthly Payment = P × (r(1 + r)^n) / ((1 + r)^n - 1)
Where:
- P = Principal loan amount
- r = Monthly interest rate (annual rate ÷ 12 ÷ 100)
- n = Number of payments (loan term in years × 12)
This formula accounts for the interest charged on the remaining balance each month, which is why the payment amount decreases over time. The total amount paid over the life of the loan is the monthly payment multiplied by the number of payments.
Note: This calculator assumes fixed monthly payments and does not account for prepayment penalties or other fees that may apply to your specific loan.
Worked Example
Let's calculate a monthly payment for a $25,000 loan at 4.5% APR over 5 years (60 months).
- Convert the annual rate to a monthly rate: 4.5% ÷ 12 = 0.375% or 0.00375 in decimal form.
- Plug the values into the formula:
Monthly Payment = $25,000 × (0.00375(1 + 0.00375)^60) / ((1 + 0.00375)^60 - 1)
- Calculate the numerator: 0.00375 × (1.00375)^60 ≈ 0.244
- Calculate the denominator: (1.00375)^60 - 1 ≈ 0.244
- Divide numerator by denominator: 0.244 / 0.244 ≈ 1
- Multiply by principal: $25,000 × 1 = $250.00
The monthly payment would be $250.00. The total amount paid over 5 years would be $250 × 60 = $15,000, with $10,000 going toward interest.
| Month | Payment | Principal | Interest | Remaining Balance |
|---|---|---|---|---|
| 1 | $250.00 | $231.68 | $18.32 | $24,768.32 |
| 2 | $250.00 | $233.36 | $16.64 | $24,534.96 |
| 3 | $250.00 | $235.04 | $14.96 | $24,300.00 |
This table shows the first three payments. Notice how the interest portion decreases while the principal portion increases.
FAQ
The APR (Annual Percentage Rate) is the total cost of borrowing, including fees and other charges. The interest rate is the actual percentage charged on the loan balance. APR is always higher than the interest rate.
A longer loan term means lower monthly payments but more total interest paid. A shorter term means higher monthly payments but less total interest.
It depends on your loan agreement. Some loans allow extra payments without penalty, while others may charge fees. Check your loan terms or contact your lender.