Interest Rate Calculator
Adjust the inputs below. Results update as you type.
How it works
Given PV, PMT, and n, solve for r using Newton-Raphson iteration (no closed form exists). For simple interest: r = I / (P × t). APY = (1 + APR/n)^n − 1. When comparing credit cards, always use APR (or APY for savings). A difference of 1% on a $300,000 30-year mortgage changes total interest by over $60,000.
Input guidance
- Use realistic rates from lender or provider quotes instead of headline averages.
- Model conservative, baseline, and optimistic scenarios before deciding.
- Include recurring real-world costs (fees, taxes, insurance, maintenance) where relevant.
The formula
Given a loan amount, payment, and term, the rate is found by solving the amortization equation for r numerically (there is no clean algebraic solution), iterating until the computed payment matches the actual payment.
Worked example
A $15,000 loan repaid at $350/month over 48 months implies an APR of roughly 6.6% — found by testing rates until the payment formula matches $350.
More examples to test
- Conservative case: use a higher interest rate and lower growth assumptions to stress-test affordability.
- Optimistic case: use a lower rate with stable income assumptions to compare upside potential.
How to interpret results
Treat this as a planning model, not a final approval tool. Compare at least two scenarios and focus on total-cost and cash-flow trade-offs.
When this can be inaccurate
Results can diverge due to fees, changing rates, tax rules, lender policies, and behavior changes that simplified models cannot fully capture.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
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Frequently asked questions
Why can't the rate be solved directly?+
The rate appears inside an exponent and a sum in the amortization formula, so it must be found by iteration (trial and error) rather than a simple rearrangement.
Is APR the same as the interest rate?+
Not quite. APR includes certain fees alongside the nominal interest rate, so it reflects the true yearly cost of borrowing more completely.
What do I need to find my rate?+
The amount borrowed, the regular payment, and the number of payments. From those three the implied periodic and annual rates can be derived.
How should I use this result?+
Treat it as a planning estimate. Compare at least two realistic scenarios, then confirm with statements, quotes, or a qualified professional before acting.
How often should I refresh assumptions?+
Refresh whenever rates, income, costs, or policy limits change materially, and before making irreversible commitments.
Guided next steps
Want the full workflow? Use this calculator inside a step-by-step guide.