Auto Loan Interest Equation and Payment Calculator

The auto loan interest equation calculates a fixed monthly payment from the amount financed, annual percentage rate (APR), and loan term; it can also estimate total interest over the scheduled payments. Enter those three values to see the payment and estimated interest, using a standard fixed-rate monthly amortization formula.

Formula

For a fixed-rate loan with equal monthly payments, the payment is calculated as:

M = P × r ÷ [1 − (1 + r)⁻ⁿ]

• M is the monthly payment in dollars.
• P is the amount financed, or principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100.
• n is the number of monthly payments: loan term in years × 12.

The calculator’s total-interest equation is I = M × n − P, where I is total interest in dollars. It uses the displayed payment rounded to the nearest cent; consequently, the estimate reflects that rounded payment multiplied by the number of installments.

Worked Example

Using the calculator’s defaults—$20,000 financed, 8% APR, and a five-year term—the monthly rate is 0.08 ÷ 12 = 0.0066667, and there are 5 × 12 = 60 payments.

1. Substitute into the payment formula: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
2. The unrounded monthly payment is about $405.53; rounded to cents, it is $405.53 per month.
3. Estimated total paid is $405.53 × 60 = $24,331.80.
4. Estimated total interest is $24,331.80 − $20,000 = $4,331.80.

Assumptions

• The APR is fixed for the entire term, and payments are equal monthly installments.
• Payments are treated as occurring at the end of each monthly period.
• Interest accrues monthly using APR divided by 12; this is the standard simplified amortization assumption.
• The calculation excludes fees, taxes, insurance, optional products, and other charges unless they are included in the amount financed.

How Auto Loan Interest Works

Each scheduled payment covers the interest accumulated since the previous payment and reduces the remaining principal. Early in a fully amortizing loan, the balance is comparatively high, so more of a payment goes toward interest. As principal falls, the interest portion generally falls too, leaving more of later payments to reduce principal. The payment formula sets an installment intended to bring the balance to zero after the stated number of payments, subject to the assumptions above.

APR is entered as an annual percentage, not as a monthly percentage. Dividing APR by 1,200 converts a percentage-per-year figure to a decimal-per-month rate. For example, 8% becomes 0.0066667 per month. Entering 0.08 as the APR would mean 0.08%, not 8%, and would produce a very different result.

What the Results Tell You

The monthly payment is the scheduled principal-and-interest installment under this model, not necessarily the full amount due on a vehicle. A lender’s payment may also reflect financed charges or other contractual details. Total interest is the estimated cost of borrowing over all scheduled installments, above the principal entered. Total payments equal principal plus interest in this simplified calculation.

For a simple comparison of loan structures, hold two inputs constant while changing the third. A larger amount financed or a higher APR raises the calculated payment when the term is unchanged. A longer term generally reduces the scheduled payment but means more payment periods; with a positive rate, that often increases total interest. These are mathematical effects, not a recommendation about which terms to choose.

Common Errors and Limits

• Using the vehicle price as the loan amount: the relevant principal is the amount financed. A down payment or trade-in can reduce it, while charges included in financing can increase it. Use the lender’s quoted amount financed when available.
• Confusing APR and monthly rate: enter APR as a yearly percentage, such as 8, rather than the decimal 0.08 or monthly rate.
• Rounding too early: keep the rate and intermediate calculations unrounded, then round the payment to cents. Small rounding differences can affect the total across many payments.
• Assuming every contract is a standard amortizing loan: irregular payment dates, variable rates, balloon amounts, deferred payments, or other arrangements may not follow this equation. A final installment can also differ slightly because of the lender’s precise accrual and rounding methods.

The formula is useful for estimating a conventional fixed-rate payment, but it cannot reproduce every contract’s exact schedule. Use the actual lender-provided APR, amount financed, term, and payment schedule for a closer estimate; check the loan disclosure for contract-specific amounts and timing.

Frequently Asked Questions

How do I calculate interest on a car loan per month?
For a simple estimate in a given month, multiply the remaining principal by the monthly rate, calculated as APR ÷ 1,200. The interest portion changes as the principal balance declines.

Is the auto loan interest equation the same as the payment formula?
The payment equation uses the interest rate, principal, and number of payments to calculate a level installment. Total interest is then estimated by multiplying that installment by the number of payments and subtracting the principal.

Does a longer car loan term lower total interest?
Not necessarily. A longer term usually spreads repayment over more installments and can lower the scheduled payment, but at a positive rate it generally increases the time interest accrues and may increase total interest.

Does this calculator include a down payment or trade-in?
Enter the resulting amount financed as the loan amount. The calculator does not separately process a down payment or trade-in, and it cannot determine the amount financed from a vehicle price without those details.

Why is my lender’s payment slightly different?
The contract may use different payment dates, daily interest accrual, fees or financed charges, or a rounding method that differs from this monthly estimate. Compare the inputs and the lender’s disclosed payment schedule.

This result is an estimate; the lender’s disclosure gives the exact figures.

Related

• Loan Calculator With Payment Amount and Total Interest
• Monthly Loan Repayment Calculator and Payment Formula
• 30 Year Loan Repayment Calculator: Monthly Payment & Interest

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2