Interest Rate Calculator
Find the implied annual percentage rate of a fixed-rate installment loan when you know the principal, the monthly payment, and the number of months.
Interest Rate Calculator tool
About the Interest Rate Calculator
The solver searches for the APR whose amortization payment matches the payment you typed — the reverse of the loan and payment calculators. Fees, prepaid interest, and non-monthly compounding are not in the equation, so a Truth-in-Lending APR can differ.
If the payment is too small to repay the principal even at 0%, there is no nonnegative APR. The calculator reports an error instead of a negative rate. A payment that is only a few cents above the zero-interest amount implies a very small APR; one that is far above implies a high rate or a short term.
How the Interest Rate Calculator works
There is no simple closed form for the rate. The tool bisects APRs from 0% to 1,000% until the standard monthly payment matches.
Find APR such that loan_payment(amount, APR, months) = payment
At 0%: payment must be at least amount ÷ months
Example
$10,000 repaid with $304.22 a month for 36 months implies about 6% APR.
How to Use the Interest Rate Calculator
- Enter the amount financed.
- Enter the monthly payment.
- Enter the term in whole months.
- Read the implied APR and the interest check.
- Compare with the rate on the offer if fees make the APR higher than the note rate.
Interest Rate Calculator Examples
Known 6% loan
Reversing $10,000 / $304.22 / 36 months returns about 6%.
0% financing
If payment × months equals the amount, the implied APR is 0.
Payment too small
$100 a month on $10,000 for 36 months cannot repay principal, so the result is rejected.
How to Solve for an Interest Rate
Guess a rate, compute the payment, and raise or lower the guess until it matches. Computers do that by bisection; a spreadsheet RATE() function is the same idea.
Sanity checks
If you already know the payment from the loan calculator, reversing it should return the same APR.
| APR | Payment |
|---|---|
| 0% | $277.78 |
| 6% | $304.22 |
| 12% | $332.14 |
When the payment includes extras
Credit-card “minimum due” and mortgage PITI are not pure amortization payments. Strip insurance, tax, and fees before you treat the leftover as P&I. For a car offer, exclude prepaid maintenance if it was bundled into the monthly figure. After you have a clean P&I payment, this page’s APR should sit close to the loan calculator’s rate for the same principal and term. A payment only a few cents above amount ÷ months implies a tiny APR; a payment that cannot cover principal even at 0% has no nonnegative rate and is rejected.
Frequently Asked Questions
Why not the same as the note rate?
Origination fees and prepaid finance charges raise a disclosed APR.
Monthly only?
Yes. This reverse solver matches the monthly loan formula.
How precise is it?
The APR is rounded to four decimal places after a tight bisection.
Can I use this for mortgages?
You can reverse P&I only. Taxes and insurance in an escrow payment will overstate the rate.
Is this credit advice?
No. It is a mathematical inverse of the payment formula.
Guides that use this calculator
- How to Calculate a Loan Payment
A fixed loan payment comes from principal, APR and months. Here is the formula, a 36-month example and when to use extra principal.