The four numbers you need
Any financing offer can be reduced to four numbers: the price, the down payment, the term in months and the monthly payment. If you know those four, the interest rate is no longer a mystery — it is the only rate that makes them add up.
In the United States the lender must also give you a Truth in Lending disclosure with the APR before you sign. Working the rate out yourself is still useful earlier on, when all you have is a quote, a screenshot or what a salesperson said.
A worked example
Say an offer reads: $28,000 car, $3,000 down, 72 months at $450 a month. No rate in sight.
- Amount financed: $28,000 − $3,000 = $25,000.
- Total you will pay: $450 × 72 = $32,400.
- Interest hidden in the payments: $7,400.
- The monthly rate that makes 72 payments of $450 worth exactly $25,000 today: 0.75 %.
- As an annual rate: 8.95 % nominal (the way APRs are quoted), or 9.32 % effective once monthly compounding is counted.
Why there is no simple formula
Going from the rate to the payment is one line of algebra. Going back is not: the rate sits both inside and outside a power, so it cannot be isolated. Calculators solve it numerically — ours uses bisection, testing a rate, checking whether the payments come out too high or too low, and halving the interval until the answer stops moving.
When the rate comes out higher than you were told
The rate you calculate covers everything that is being paid off through the monthly payment. If extras — a service contract, gap coverage, fees — have been rolled into the loan, they are inside the payment too, and the rate worked out from the car's price will be higher than the lender's rate on the real amount financed.
In the example above, if $1,500 of extras were financed on top of the car, the lender's rate on $26,500 would be 6.86 % nominal, not 8.95 %. Same payment, different story. A gap like that is a good reason to ask for the itemised amount financed.
Try it with your own offer
Type the four numbers into «Find the rate» and you get the monthly, nominal and effective rates, plus the total interest and total outlay. Nothing you type leaves your browser.