Interest Rate Calculator
Find the annual interest rate implied by a loan's amount, monthly payment and term. Useful for reverse-engineering an offer to compare it against other quotes.
Enter loan details
Enter loan details and press Find interest rate.
How the rate is found
There is no closed-form algebraic solution for the interest rate in the amortization formula. This calculator uses a numerical method (bisection search) to find the annual rate that makes the present value of all payments equal to the loan amount.
P = M · [ 1 − (1 + r)^-n ] / r
Where r is the rate per period and n is the total number of payments.
Related calculators
Frequently asked questions
The formula contains the rate in the denominator and inside an exponent, so it cannot be algebraically rearranged to isolate the rate. Numerical methods converge quickly and give a very accurate result — accurate to within 1/1000 of a percent.
No. This calculator returns the interest rate implied by the numbers you enter. APR also includes mandatory fees (origination, closing, etc.), so it is usually higher. Use the APR calculator if you have fee details and need the true annual cost.