A car loan payment equals principal times the monthly interest rate, divided by one minus (1 plus the monthly rate) raised to the negative number of payments. A $24,000 loan at 6.9% APR over 60 months produces a payment of $474.10 a month, for $28,445.84 paid in total, of which $4,445.84 is interest.
What is the worked example for a $24,000 loan?
Convert 6.9% APR to a monthly rate: 0.069 ÷ 12 = 0.00575. Raise (1 + 0.00575) to the 60th power: 1.4105954, so its reciprocal is 0.7089205. Subtract from 1: 0.2910795. Multiply principal by the monthly rate: 24,000 × 0.00575 = 138.00. Divide 138.00 by 0.2910795 to get 474.10, the level monthly payment. Keep the full precision of the power term: rounding it to five decimals here shifts the payment by four cents, and that error then travels through every total on the page. Multiplying 474.10 by 60 gives 28,445.84 total paid; subtracting the 24,000 principal leaves 4,445.84 in interest.
How do I calculate a car loan payment myself?
The formula is M = P × r ÷ (1 − (1 + r)⁻ⁿ), where P is the amount financed, r is the interest rate expressed as a monthly decimal, and n is the number of monthly payments. Convert the advertised annual percentage rate to a decimal with the percentage calculator, then divide by 12 before it enters r. n must count months, not years, so a 5-year loan uses n = 60.
What should I check before trusting the number?
Confirm r is a small monthly decimal, not the annual percentage itself: entering 6.9 instead of 0.00575 produces an absurd payment. Confirm the exponent is negative; dropping the sign inverts the bracket and gives a payment far too low. A quick sanity check is that total payments (M × n) must exceed the principal by roughly the stated finance charge, never by less.
What mistakes produce a wrong payment?
A frequent mistake is using the annual rate directly as r without dividing by 12. Another is computing payment as principal divided by term, which ignores interest entirely and understates the true amount. Fees, extended warranties, or negative equity rolled into the loan increase P and are easy to leave out of a quick estimate. Rounding r to two decimal places before raising it to the 60th power also introduces a visible error.
What does this formula not cover?
This formula describes a fixed-rate, fully amortizing simple-interest loan with equal monthly payments. It does not model precomputed-interest contracts, variable-rate loans, balloon payments, or add-on interest methods, and it excludes sales tax, registration fees, and dealer add-ons unless they were folded into the financed principal beforehand. Read the contract’s own payment schedule for the binding figure.
Source for the external fact
The Consumer Financial Protection Bureau explains that an auto loan payment is split between principal and interest according to an amortization schedule set at the start of the loan in its amortization explainer.
A second worked example: $35,000 at 5.4% APR for 72 months
The same formula applies to any principal, rate, and term. Convert 5.4% APR to a monthly rate: 0.054 ÷ 12 = 0.0045. Raise 1.0045 to the 72nd power, take its reciprocal, subtract from 1, multiply the principal by the monthly rate, and divide: the level payment is $570.19. Over 72 months that is $41,053.65 paid in total, of which $6,053.65 is interest — more interest in dollar terms than the $24,000/60-month example above even though the rate is lower, because the term runs 12 payments longer and the principal is larger.
How the payment changes across common loan terms
Holding the $24,000 principal and 6.9% APR from the worked example constant and changing only the term shows how a longer schedule lowers the monthly payment while raising total interest.
| Term | Monthly payment | Total paid | Total interest |
|---|---|---|---|
| 36 months | $739.95 | $26,638.33 | $2,638.33 |
| 48 months | $573.60 | $27,532.66 | $3,532.66 |
| 60 months | $474.10 | $28,445.84 | $4,445.84 |
| 72 months | $408.02 | $29,377.78 | $5,377.78 |
Each row uses the identical formula with only n changed. The monthly figure keeps falling as the term extends, while total interest keeps rising because the balance is carried for more months at the same monthly rate.
What happens to the formula at 0% APR financing
When an offer advertises 0% APR, the monthly rate r is 0, and the formula’s denominator, 1 − (1 + r)⁻ⁿ, also becomes 0 — a division the standard formula cannot evaluate. At 0% the payment is simply principal divided by the number of months: $24,000 over 60 months is 24,000 ÷ 60 = $400.00 a month, with no interest added. A calculator built only around the interest-rate version of the formula needs a separate branch for this case rather than a very small rate substituted for zero.
How to check the payment with a present-value calculation
A level payment can be checked by working backward: discount each of the 60 payments of $474.10 to today’s value at the 0.575% monthly rate and add the results. Payment 1 is worth 474.10 ÷ 1.00575 ≈ 471.39 today; payment 60 is worth 474.10 ÷ 1.00575⁶⁰ ≈ 336.13. Summing all 60 discounted payments returns $24,000 to within a cent, which is the point of the check: if the sum comes back noticeably short or long, the payment, the rate, or the number of periods is wrong rather than merely rounded.
How this differs from a lease payment
This formula amortizes the full financed price down to zero. A lease payment is built differently: from the vehicle’s expected depreciation over the lease term, plus a finance charge calculated on the amount financed and the value the leasing company expects the vehicle to retain at the end. The Consumer Financial Protection Bureau explains that leasing finances the vehicle’s expected loss of value while it is driven, not its full price, which is why a lease payment on the same vehicle is not directly comparable to an amortized loan payment of the same dollar figure — see its leasing-versus-buying guidance.
How much a rounded monthly rate can distort the payment
The monthly rate itself needs to stay precise, not just the final payment. 6.9% APR gives an exact monthly rate of 0.00575. Rounding that to three decimal places, 0.006, before raising it to the 60th power changes the computed payment from $474.10 to $477.50 — a difference of $3.40 a month that compounds to about $204 over the 60-month term. The error comes entirely from rounding r too early; rounding only the final dollar-and-cent payment, after the full calculation, does not cause this drift.
Total interest across a range of rates, same principal and term
Holding the $24,000 principal and 60-month term fixed and changing only the APR shows how much the interest cost alone moves with the rate.
| APR | Monthly payment | Total interest |
|---|---|---|
| 3.9% | $440.91 | $2,454.86 |
| 6.9% | $474.10 | $4,445.84 |
| 9.9% | $508.75 | $6,524.94 |
| 12.9% | $544.85 | $8,690.76 |
Between the lowest and highest rate shown, total interest more than triples for the identical loan amount and term.
Where a $24,000 financed principal actually comes from
The formula only ever sees one number, P, but that number is usually a vehicle price adjusted by several other amounts first. A $28,000 vehicle price, minus $3,000 of trade-in equity and a $1,000 manufacturer rebate, leaves $24,000 to finance — the same principal used throughout this guide’s worked example. Sales tax, a documentation fee, or negative equity carried over from a previous loan would instead add to that $24,000 before it is entered into the payment formula, which is why two buyers financing “the same car” at the same price can end up with different principals and different payments.
Related calculators
Convert an advertised rate to a decimal with the percentage calculator, see how the same 60 payments split between interest and principal in the amortization schedule guide, and work backward from a budget in the loan-amount guide.