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● Reverse rate calculation

Find Interest Rate Calculator

Know the payment and balance but not the rate? This calculator works backwards to find the implied interest rate in any loan or investment.

If a dealer offers you a $20,000 car for $450/month for 48 months, the implied interest rate is 6.4% APR. This calculator finds the hidden rate in any loan, investment, or financing offer — using numerical root-finding on the payment formula.

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Find Interest Rate Calculator
Loan: principal + payment + months → rate | Investment: start + end + years → rate
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Mode

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Loan details

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months
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Implied rate

Annual interest rate (APR)
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Monthly rate
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Total paid
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Total interest cost
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How it's calculated

Numerical root-finding: Newton-Raphson

For loans, we solve for the monthly rate r that satisfies the payment formula. Since the equation can't be rearranged algebraically, the calculator uses iterative numerical approximation:

Loan payment formula: PMT = P × r / (1 − (1+r)^-n) Solve for r: Newton-Raphson iteration r_(k+1) = r_k − f(r_k) / f'(r_k) where f(r) = P × r − PMT × (1 − (1+r)^-n) Investment (lump sum, no contributions): CAGR = (Final / Initial)^(1/years) − 1 (exact closed-form solution)
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    Rate per period
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  2. 2
    Annualized rate
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APR (Annual Percentage Rate)
The annualized interest rate for a loan, calculated as monthly rate × 12. Different from APY which includes compounding.
CAGR (Compound Annual Growth Rate)
The year-over-year growth rate that brings an investment from its starting value to its ending value. Smooths out volatility to show the implied annual return.
Newton-Raphson
An iterative numerical method for finding roots of equations. Used here because the loan rate equation has no closed-form algebraic solution.

🔢 Worked example

A $1,000 item offered as 10 payments of $120 ($1,200 total) looks like '20% interest,' but the rate baked into the payments is about 3.5% per month — over 51% per year.

Disclaimer: the found rate is the mathematical implied rate. Actual loan APR may differ if fees are included in payments or excluded. Always verify with your lender's official disclosure. Always confirm with an official source before deciding.

Frequently asked questions

How do I find the interest rate of a loan?
Enter the principal (amount borrowed), monthly payment, and number of payments. The calculator finds the monthly rate that satisfies the standard amortization formula using Newton-Raphson iteration, then converts to annual APR.
What is CAGR?
Compound Annual Growth Rate — the steady annual rate that would take an investment from its initial value to its final value over the holding period. CAGR = (Final ÷ Initial)^(1/years) − 1. It smooths out year-to-year volatility to show the overall implied return.
When would I use this calculator?
Whenever a loan or financing offer gives you payments and amounts but not the rate; or when you want to verify that a stated rate matches the actual payments. Also useful for finding the implied return of an investment that went from amount A to amount B over a known period.
What if the calculator can't find a rate?
This happens if the numbers are inconsistent — for example, a monthly payment less than the first month's interest means the loan can never be paid off. Or if the payment is exactly equal to the principal divided by months (0% rate). Check that your payment exceeds the interest portion.
Why do lenders hide the true rate?
Sometimes they don't hide it — but the stated rate may exclude fees, insurance, or use a different compounding convention. This calculator finds the true effective rate implied by the actual numbers, which may be higher than the advertised nominal rate.
When would I use a reverse interest rate calculator?
When a seller tells you 'buy now for $0 down and $X/month for Y months' without disclosing the rate. Or when comparing a lease vs. loan with different total amounts. Or to verify that a stated rate matches the actual payments.
Are my results saved? Do I need an account?
No account or sign-up needed. Every calculation is saved automatically in your own browser, and you can also pin a result with the save button. Nothing is sent to any server: the data stays on your device and can be erased at any time with the clear button.
How do I track my progress over time?
From the fourth entry onward a “View comparison chart” button appears, opening a line chart with every entry in time order plus an indicator panel: total change, average per entry, lowest and highest value and the period covered. You can also export the history as CSV.

About this calculator

The find interest rate calculator works backward from the numbers you already know — the amount invested or borrowed, the final value and the time period — to solve for the interest rate that connects them. It is handy when a deal quotes totals or payments but not the actual rate.

Knowing the effective rate lets you compare offers on equal footing and spot when a seemingly small payment hides an expensive rate. Because it is derived from the values you enter, double-check that those figures are accurate so the resulting rate reflects your real situation.

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By Vinicius Fonseca · Reviewed against official sources · Updated Jul 2026 · How we calculate →