Interest Rate Calculator
Work out the interest rate on a loan when you know the amount, the payment and the term, but not the rate itself.
How to use this calculator
- 1Enter the loan amount and how many years you have to pay it off.
- 2Enter the actual monthly payment — from an offer letter, a private loan, or an old statement without a stated rate.
How the calculation works
Solve r in: Payment = P × r / (1 − (1 + r)⁻ⁿ)- P
- Loan amount
- r
- Interest rate per month (unknown — what we solve for)
- n
- Total number of payments
There is no closed-form algebraic solution for r, so this uses bisection: since a higher rate always produces a higher payment for the same loan and term, the search can repeatedly halve the range until it converges.
Worked example
$20,000 borrowed, $450 a month, over 5 years
- 1.Total paid over 60 months: 450 × 60 = $27,000, so total interest is $7,000 — 35% of the amount borrowed.
- 2.Searching for the monthly rate that makes the annuity formula produce exactly $450 a month lands on a nominal annual rate of about 12.50%.
Result: About 12.50% APR
What an interest rate is actually pricing
An interest rate is the price of money over time. To a borrower it is the cost of using someone else's money now instead of saving up; to a lender it is the compensation for giving up the use of their own money, plus a cushion for the risk that it might not come back in full. Every loan, from a mortgage to a store credit card, is built around this same trade — the rate just sets how steep the price is.
Rates are not arbitrary. They generally track the lender's own cost of funds, the perceived risk of the borrower, and how long the money is tied up for — which is why a short car loan, a decades-long mortgage, and a same-day payday loan can carry wildly different rates even from the same lender.
APR, APY and effective rate are not the same number
The word "rate" hides several distinct figures, and mixing them up is one of the easiest ways to misjudge a deal.
- Nominal (annual) rate — the headline percentage, before accounting for how often interest compounds. This is what most loan offers quote up front.
- Effective annual rate — what the nominal rate actually costs once compounding is factored in — always equal to or higher than the nominal rate for the same loan, because interest that compounds monthly is charged on previously accrued interest too.
- APR (annual percentage rate) — in lending, a rate meant to include certain fees alongside interest, giving a fuller picture of borrowing cost — though what counts as a fee varies, so two lenders' quoted APRs are not always perfectly comparable.
Why you sometimes have to solve for the rate yourself
Most consumer loans disclose the rate clearly, but plenty of real-world financing does not. Dealer and in-house financing is sometimes quoted purely as "$X a month," private and family loans are often agreed informally around a payment figure rather than a rate, and older loan paperwork can simply be missing the number entirely. In every one of these cases, the amount borrowed, the payment, and the term are known — only the rate is not — which is exactly the reverse-engineering problem this calculator solves.
Using a rate you have found to judge a deal
Once you know the true rate on a loan, the useful next step is comparison, not just curiosity. Weigh it against rates currently available from banks and credit unions for a similar loan type, term and credit profile — a private or dealer-financed rate that comes out far above the going market rate for a comparable loan is worth negotiating on or refinancing away from. A rate that looks unusually low is worth checking for a shorter-than-expected term or a larger-than-expected payment doing the work instead.
What this assumes, and where it stops
Assumptions
- The payment is level and monthly, and the rate is constant for the whole term (a standard fixed-rate amortising loan).
Limitations
- Cannot back out a rate for loans with irregular payments, balloon payments, or rates that change during the term.
Common questions
Why would I not just be told the interest rate?
It happens more often than you would expect: private or family loans, older loan documents that only quote the payment, dealer financing quoted purely as "$X a month," or lease agreements. This backs the rate out from what you actually know.
Is the answer exact?
Yes, to well beyond any practical precision — the search (bisection) narrows the range by half at each step for 200 steps, which converges far tighter than a real-world payment is ever rounded to.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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