Interest Rate Calculator
Enter loan principal, equal monthly payment and payment count to infer the monthly rate and its annual equivalents.
Calculator arithmetic runs locally in your browser and does not require an API.
The interactive calculator loads here when JavaScript is enabled.
How to use Interest Rate Calculator
Use an unrounded payment when available. The loan must reach zero balance with equal end-of-month payments; fees and irregular payments are excluded.
Formula and method
Solve P = M[1 − (1+r)^−N]/r numerically. Nominal annual rate = 12r; effective annual rate = (1+r)^12 − 1.
Understanding the results
Nominal annual rate scales the monthly rate; effective annual rate accounts for monthly compounding. This is not a fee-inclusive APR. A payment below P/N has no supported nonnegative rate.
Worked example
For principal 10,000, payment 188.7123364401 and 60 months, the inferred nominal annual rate is approximately 5%; monthly rate is approximately 0.416667%.
These are mathematical estimates, not financial advice or an offer of credit.
Frequently asked questions
Does the result include fees as APR?
No. It infers an interest rate from principal and payments without origination fees or other charges.
Why does a rounded payment change the result?
The solver treats the entered payment as exact; rounding it changes the cash-flow equation slightly.
What if payment is below principal divided by months?
There is no nonnegative rate that fully repays the loan under these assumptions.