Loan Tools
Interest Rate Calculator
Work backwards from a loan payment to find the implied interest rate. If you know the loan amount, your monthly payment, and the loan term, we'll calculate the APR the lender is charging.
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Loan details
Summary
Loan details
How we find the implied rate
01
Enter loan details
Input the original loan amount, your monthly payment, and the loan term in years.
02
Iterative solving
We use Newton-Raphson numerical iteration to find the monthly rate that produces exactly your payment.
03
See your APR
The monthly rate is converted to annual APR and effective annual rate for easy comparison.
Frequently asked questions
When would I use this calculator? ▼
Use it when a lender gives you a payment quote but doesn't clearly disclose the APR. Enter the quoted payment to verify the true rate. Also useful for analyzing older loan documents or peer-to-peer lending.
What's the difference between APR and effective annual rate? ▼
APR (Annual Percentage Rate) is the nominal rate — 12× the monthly rate. The effective annual rate (EAR) accounts for compounding: EAR = (1 + monthly rate)^12 - 1. EAR is always slightly higher than APR when compounding monthly.
Why might there be no solution? ▼
If your monthly payment is too low to cover even the interest for the first month, no valid interest rate exists. Make sure payment × term > loan amount (you must pay back at least the principal).
Disclaimer: Results are mathematical estimates. The actual APR on a loan may differ if origination fees or other charges are included. Always request the full disclosure from your lender.
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