How to Calculate a Car Payment
The exact formula lenders use, worked through step by step with a real example.
The car payment formula is M = P x r / (1 - (1 + r)^-n), where P is the financed amount, r is the monthly rate, and n is the number of months. Financing $30,000 at 7 percent APR for 60 months: r = 0.005833, n = 60, and the payment is about $594 per month.
The formula
Auto lenders use the standard amortization formula: M = P x r / (1 - (1 + r) raised to the power of -n). P is the financed amount: price minus down payment minus trade-in equity, plus anything rolled in. r is the monthly rate: APR divided by 12. n is the term in months.
It assumes a fixed APR, monthly compounding, and equal payments. Given the same inputs, your hand calculation matches the lender's disclosure to the penny.
Worked example
Price $35,000, down payment $5,000, no trade-in: P = $30,000. APR 7 percent: r = 0.07 / 12 = 0.0058333. Term 60 months: n = 60. Compute (1.0058333)^-60, which is about 0.7054. Then 1 - 0.7054 = 0.2946. Numerator: 30,000 x 0.0058333 = 175. Divide: 175 / 0.2946 = about $594.04 per month.
Sanity check: $594.04 x 60 = $35,642 in total payments. Minus the $30,000 financed, total interest is $5,642. If a dealer's quote differs by more than a dollar, an input differs: usually the APR, the term, or fees rolled into the financed amount.
The quick dealership estimate
For mental math on the lot, use this shortcut: every $1,000 financed at 7 percent for 60 months costs about $19.80 a month. So $30,000 financed is roughly 30 x $19.80 = $594. At 5 percent it is about $18.87 per thousand; at 10 percent about $21.25.
The shortcut gets you within a few dollars, close enough to spot a padded payment quote. For the exact number, use the calculator.
What the formula leaves out
The formula covers the loan only. Sales tax, title and registration, dealer documentation fees, and insurance are separate, though dealers often roll the first three into the financed amount, which the formula then includes automatically via the larger P.
It also ignores the time value of incentives: a $2,000 rebate reduces P directly and is almost always worth more than it looks, because it also reduces every interest charge computed on P.
Skip the arithmetic
Skip the hand math: the free auto loan calculator runs the same formula instantly.
Payment math questions
What is the car payment formula?
M = P x r / (1 - (1 + r)^-n), where P is the financed amount, r is the APR divided by 12, and n is the term in months. It assumes a fixed rate and equal monthly payments.
How do I estimate a car payment quickly?
Use the per-thousand shortcut: at 7 percent for 60 months, every $1,000 financed costs about $19.80 a month. Multiply by your financed thousands: $30,000 financed is roughly 30 x $19.80 = $594 a month. Adjust up or down for different rates.
Why is the dealer's payment higher than my calculation?
Almost always because the financed amount is larger than the price you used: sales tax, title and documentation fees, extended warranties, or negative equity from a trade-in get rolled into the loan. Ask for the itemized amount financed and rerun the formula on that number.