Online Tool Store
Interest Rate Solver
Solve for the periodic and annual interest rate of a loan when you know the principal, payment amount, and term, using iterative numerical solving in your browser.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Monthly interest rate
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Annual (APR) rate
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How the Interest Rate Solver works
- Enter the loan's original principal, the fixed monthly payment, and the term in months.
- The tool runs a bisection search on the standard amortizing-loan payment formula, testing candidate rates until the computed payment matches yours.
- It reports both the monthly periodic rate and the equivalent simple annual (APR-style) rate.
The formula being solved
For a fixed monthly rate r, principal P, and n payments: Payment = P × r / (1 − (1 + r)^−n). The solver searches for the r that makes this equation true for your entered payment.
FAQ
Why solve for the interest rate instead of computing a payment?
Most loan calculators go the other direction — rate, principal, and term in, payment out. This tool is for the reverse case: you already know the payment, principal, and term (e.g. from an offer letter) and want to know the implied interest rate.
How is the rate actually solved?
There is no closed-form algebraic solution for rate in the standard amortization formula, so the tool uses bisection: it repeatedly narrows a range of possible rates, checking which one produces your exact monthly payment, until it converges to three decimal places.
Why might my payment never reach a valid rate?
If your monthly payment times the term is less than or equal to the loan amount, no positive interest rate could ever produce that payment — you would need a higher payment or a longer term.
How we compare
| Feature | Online Tool Store | Spreadsheet RATE() function | Manual trial and error |
|---|---|---|---|
| No spreadsheet needed | ✓ | ✗ | ✓ |
| Fast, accurate convergence | ✓ | ✓ | ✗ |
This solves the base periodic rate — real-world APR disclosures may include fees that this simplified formula doesn't account for.