Car Loan Payment Calculator

A car loan is an amortized loan: the payment is the same every month, and each payment first covers the interest that accrued that month, with whatever is left reducing the balance.

$M = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}$

• $P$ — the amount financed (the principal), not the sticker price
• $r$ — the periodic rate: the annual rate divided by 12 for monthly payments
• $n$ — the total number of payments (years $\times$ 12)
• $M$ — the level monthly payment

The formula comes from setting the present value of $n$ equal payments equal to the amount borrowed and solving that geometric sum for $M$. If $r = 0$ (a true 0% promotion) the expression is undefined and the payment is simply $M = P/n$.

AI-Math is a math solver, not a lender. Rates, sales tax and financing rules differ by lender and by jurisdiction and change over time, so take those numbers from your own quote or loan documents — the formula then does the rest.

1. Find the amount financed

$P = \text{price} + \text{sales tax} + \text{fees} - \text{down payment} - \text{trade-in}$

Sales tax rules vary by state and even by county, and some places tax the price after the trade-in credit. Use the rate and rule on your own paperwork.

2. Split each payment

For any month, with $B$ the balance at the start of that month:

$\text{interest} = B \times r, \qquad \text{principal} = M - \text{interest}$

Repeating this for every month is the amortization schedule. Early payments are mostly interest because $B$ is large; late payments are almost all principal.

3. Total interest

$\text{total interest} = nM - P$

4. Reverse the formula

Given a payment you can afford, the loan it supports is

$P = M \cdot \frac{(1+r)^n - 1}{r(1+r)^n}$

And the number of months to clear a balance at payment $M$ is

$n = \frac{-\ln\!\left(1 - \frac{rP}{M}\right)}{\ln(1+r)}$

which is how you measure what an extra payment actually buys you.

• Using the annual rate directly: a 6% APR is $r = 0.005$ per month, not $0.06$. Forgetting to divide by 12 inflates the payment enormously.
• Financing the sticker price: tax, title and fees go up, the down payment and trade-in go down. Only the net figure is $P$.
• Confusing rate with APR: the APR folds in certain finance charges, so a payment computed from the nominal rate can differ slightly from one computed from the APR. Use whichever your contract bases the payment on.
• Multiplying principal by rate by years: that is simple interest and it overstates the cost of an amortizing loan, because the balance falls every month.
• Rounding the payment then reusing it loosely: lenders round $M$ to the cent, so the final payment is usually a few dollars off. Always let the last row of the schedule absorb the difference.
• Ignoring how extra payments are applied: an extra amount only shortens the loan if the lender applies it to principal rather than to the next scheduled payment.