Find the Rate Implied by Equal Monthly Payments
This tool solves the fixed-payment loan equation from the amount financed, number of monthly payments and principal-and-interest payment. It assumes the first payment is one month after borrowing and the balance reaches zero after the last payment.
How to Use the Calculator
- Enter the amount financed after any down payment. Use the same currency for principal and payments; display amounts are in dollars.
- Enter a term in years or months that converts to a whole number of months, up to 1,200.
- Enter the monthly principal-and-interest payment. Exclude escrow, property taxes, insurance and separate fees.
- Select Calculate. Afterward, edits update the result. Hide Results collapses the output without changing inputs.
Formula and Rate Convention
For monthly rate r and n payments, principal = payment × [1 − (1 + r)−n] / r. At r = 0, principal = payment × n. A bounded bisection solver searches rates from 0% to 100% nominal annual and checks the payment residual before returning a result.
The displayed annual rate is 12 × r. An effective annual rate would instead be (1 + r)12 − 1. Neither is an inflation-adjusted real rate. This tool does not calculate regulatory APR because it does not model fees and dated cash flows.
Read the Amortization Schedule
Each row shows payment, interest, principal repaid and remaining balance. Under a positive fixed rate, interest declines as the balance falls. This does not mean early payments must be mostly interest. At zero interest, the entire payment reduces principal.
Totals are summed from the displayed model schedule. Values are calculated without rounding each month and displayed to cents; a lender may use different payment rounding or day counts. Rates are displayed to three decimals, which is presentation precision rather than a guarantee about a loan quote.
Model Limits
This is a fully amortizing, monthly model. It does not handle variable rates, interest-only periods, balloon payments, extra repayments, daily interest accrual or fees. It does not predict which rate a lender will offer or whether borrowing is affordable. The input and rate limits are calculation boundaries, not legal lending limits.
References: the CFPB explains interest rate versus APR, principal-and-interest versus total monthly payments, and amortization.
Frequently Asked Questions
Which rate does this calculator return?
The nominal annual rate is 12 times the solved monthly rate. Payments occur at each month-end and fully repay the loan. The result is not an inflation-adjusted real rate, effective annual rate or a regulatory APR.
Which payment should I enter?
Enter only the fixed principal-and-interest payment. Exclude taxes, insurance, escrow and separate fees. Use the amount financed, not the purchase price before a down payment.
What is the difference between interest rate and APR?
APR accounts for interest and certain additional borrowing costs under applicable disclosure rules. This tool has no fee or payment-date inputs and does not calculate a disclosed APR.
Which loans fit the model?
A fully amortizing loan with equal end-of-month payments and one constant nonnegative rate fits this model. Variable rates, daily accrual conventions, balloon payments, deferred payments and extra payments require other calculations.
Why might no result be returned?
Use positive finite amounts up to $1 trillion and a term that converts to 1–1,200 whole months. Total payments must at least equal principal. The supported nominal annual rate range is 0–100%; out-of-range or numerically unresolved inputs return no result.
Why can the schedule differ from my lender?
The model uses unrounded monthly arithmetic and displays cents. Contractual day counts, payment dates, fees and rounding can change the lender schedule. At a positive rate, the interest share declines as principal is repaid; it need not be most of the early payment.