Interest Rate Calculator
Given a loan amount, monthly payment and term, solve for the interest rate. Useful for reverse-engineering a quoted payment, comparing offers or checking lender math.
How to use the Interest Rate Calculator
- Enter your inputs into the Interest Rate Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The interest rate solver
No closed form — solved iteratively from M = P · r(1 + r)^n / ((1 + r)^n − 1)
Because r appears multiple times non-linearly, no algebraic solution exists. The calculator uses numerical iteration (Newton's method or bisection) to converge on the rate that makes the payment formula balance.
Worked example
A $20,000 loan with a $400 monthly payment over 60 months implies an interest rate of about 7.43% APR. If the payment is $450 instead, the rate jumps to about 12.92% APR.
Frequently asked questions
Why solve for the rate instead of the payment?
When comparing lenders that quote you a flat monthly payment without an APR, or when you have an existing loan and want to verify the rate, you need to back into the rate from the payment.
Is this the APR or the simple interest rate?
The calculator returns the periodic rate annualized. For loans with origination fees or points, the APR — which includes those fees — will be higher than the rate this returns from the payment alone.
Can I use this for credit cards?
Not directly, because credit card minimum payments vary with the balance. Use a fixed monthly payment for any payoff scenario you're actually solving.