Interest Rate Calculator
Solve the nominal annual rate implied by a fixed loan principal, monthly payment, and term.
Content updated August 4, 2026
This solves an interest rate, not APR. It omits origination charges, closing costs, and other fees that can make APR different.
Solve the nominal annual interest rate implied by a known loan principal, equal monthly payment, and repayment term. This reverses the standard fixed-payment amortization formula rather than asking you to supply the rate.
The result is designed for a fully amortizing closed-end loan with end-of-month payments and no fees. It also shows the monthly rate, total of payments, total interest, and the zero-rate payment boundary so you can inspect the result.
The Interest Rate formula
Payment = P × r ÷ [1 − (1+r)^−n] · nominal annual rate = 12r × 100%P = principal · r = monthly decimal interest rate · n = whole number of equal monthly payments · at r = 0, payment = P/n.
Worked example
A 10,000 principal repaid by 60 monthly payments of about 188.712336 implies a monthly rate of about 0.416667% and a nominal annual interest rate of 5%. Total payments are about 11,322.74, so total interest is about 1,322.74.
Assumptions, rounding, and limitations
Assumptions
- The loan has one fixed interest rate and equal end-of-month payments that fully amortize the principal.
- Interest accrues monthly at the nominal annual rate divided by 12.
- There are no upfront or ongoing fees, financed charges, extra payments, missed payments, residual value, or balloon payment.
- The entered term equals a whole number of monthly payments.
Rounding: Bisection runs for 120 iterations and retains the solved floating-point rate. The annual display rounds to four percentage decimals, the monthly display to six, and currency totals to two decimals.
Limitations
- Only nonnegative nominal annual rates through 100% and terms through 1,200 months are supported.
- Does not calculate APR or model daily interest, irregular payment dates, compounding other than monthly, fees, variable or introductory rates, or lender-specific rounding.
- The result is an equation solution, not a loan quote, disclosure, approval, or financial recommendation.
Sources
- Interest Rate and APR: What’s the Difference? — Consumer Financial Protection Bureau
- How Does Paying Down a Mortgage Work? — Consumer Financial Protection Bureau
How the rate is solved
For a positive monthly rate, the fixed payment equals principal multiplied by r and divided by 1 − (1+r) raised to negative n, where r is the monthly rate and n is the number of payments. At zero interest the payment is simply principal divided by n.
There is no simple elementary rearrangement for r, so the engine uses bounded bisection. The payment rises monotonically with a nonnegative rate, allowing the solver to repeatedly narrow the interval from 0% through the documented 100% nominal annual limit.
Interest rate is not the same as APR
The CFPB explains that a loan's interest rate is the borrowing cost paid to the lender, while APR includes the interest rate plus additional loan fees. Because this calculator has no fee input, its solved result should not be labeled or compared as APR.
Real disclosures can also use different timing, day-count, compounding, rounding, residual, balloon, introductory, or variable-rate rules. Use the lender's contract and legally required disclosures for an actual transaction.
Frequently asked questions
▶What inputs do I need to solve a loan interest rate?
Enter the original principal, the equal fixed monthly payment, and the number of whole monthly payments.
▶Why can a monthly payment be too low?
At a nonnegative interest rate, the smallest fully amortizing payment is principal divided by the number of months. A lower payment cannot repay even the principal in that term.
▶Is the result an APR?
No. It is a nominal annual interest rate. APR can include origination charges and other fees that this tool does not accept.
▶How are years converted to months?
Years are multiplied by 12 and must produce a whole number of monthly payments. You can also enter the term directly in months.
▶Can this solve a variable-rate or balloon loan?
No. The payment formula assumes one fixed rate, equal end-of-month payments, and a zero balance after the final scheduled payment.
Related calculators
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Open calculator →Build a year-by-year schedule for a fixed-rate, fully amortizing loan.
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Open calculator →Disclaimer: Interest Rate Calculator results are estimates for general information and education only, and are not financial, tax, legal or medical advice. Verify important decisions with a qualified professional.