Interest Rate Calculator — the rate your payment implies

How it works

The amortization formula M = P·r(1+r)ⁿ ⁄ ((1+r)ⁿ − 1) gives the payment from the rate; this page inverts it. The payment rises steadily as the rate rises, so the inversion is a simple search: try a rate, compute its payment, adjust up or down until the computed payment matches yours — bisection, accurate to far beyond the displayed precision. Two boundaries frame it: a payment of exactly the loan divided by the months means 0% (no interest at all), and a payment at or above the whole loan is not really a loan. The totals then follow from arithmetic alone — every payment summed, minus the amount borrowed — and the table shows the payment at rates half and one point either side of the implied one, the shopping spread read forward again.

Worked example

The inversion runs on a published pair: LibreTexts works a $250,000 loan at 6% over 30 years to a payment of $1,498.88 — so feeding $250,000, $1,498.88, and 30 years into this page recovers 6.00%, the same published pair read backwards. On the default inputs — the same loan at a round $1,500 a month — this calculator solves an implied rate of about 6.01% and roughly $290,000 of total interest, its own computation for those inputs; only the 6% pair is a published value (LibreTexts).

Frequently asked questions

When would I need to solve for the rate?

Whenever an offer arrives as a payment instead of a rate: dealer financing quoted monthly, a payment plan, an old statement without paperwork, or a seller-financed deal. The payment, amount, and term pin the rate exactly — this page recovers the number so you can compare it against quoted rates elsewhere.

How does the calculator find the rate?

By search rather than algebra: the amortization formula cannot be rearranged for the rate in closed form, but a higher rate always means a higher payment, so the calculator repeatedly halves the interval between too-low and too-high until the payment matches yours. The result is exact to well beyond the two decimals displayed.

Why does it say no rate exists?

Two honest boundaries. If your payment times the number of months equals the loan, the rate is 0% — nothing was charged. If the payment is at or above the entire loan amount, a single payment would clear it and the term is fiction; the calculator reports the degenerate case rather than inventing a number.

Is the implied rate the same as the APR?

No — this page recovers the note rate from principal and payment alone. An APR folds fees and other borrowing costs into an effective rate on what you actually received, so it is usually higher; the APR calculator does that computation with the same solver.

What does the rate table show?

The implied rate with rates half and one percentage point either side, each with its payment and lifetime interest on your loan. It is the sensitivity view: what shopping a slightly better rate is worth per month, and what a slightly worse one costs over the term.

How is this different from the loan calculator?

The loan calculator goes forward — rates in, payments out, scenarios side by side. This page goes backward from a payment you already have. They meet in the middle: recover a rate here, then compare it against alternatives there.

How accurate is this, and what does it exclude?

The recovered rate is mathematically exact for a fixed-rate, fully amortizing loan with the payment you entered. It excludes fees (that is the APR's job), taxes and insurance bundled into a total payment — enter the principal-and-interest portion only — and variable-rate loans, where no single implied rate exists.