Solve for the interest rate on a loan when you know the amount, the monthly payment, and the term. Reverse-engineer the rate behind any fixed loan or financing offer.
Find the rate from the payment
Sometimes you know the loan amount, the monthly payment, and the term, but not the interest rate — for example, when a dealer or lender quotes only a payment. This calculator solves the amortization equation backward to find the annual interest rate that produces that exact payment. It's the inverse of a normal loan calculator and is useful for checking quotes, comparing financing offers, and spotting hidden costs baked into a "low monthly payment."
For the math to work, the monthly payment must be high enough to repay the loan over the term — at minimum the loan amount divided by the number of months (which corresponds to a 0% rate). If the payment is lower than that, no positive interest rate can amortize the loan, and the calculator will flag it. Once solved, it also shows your total amount paid and total interest.
Enter loan amount, monthly payment, and term to find the implied annual interest rate behind a quoted payment.
Dealers often quote a payment, not a rate. Reverse-solving reveals the real rate so you can compare and negotiate.
The payment must exceed loan ÷ months (the 0% case). Below that, the loan can't be repaid and no rate exists.
Finding the interest rate implied by a known payment, principal and term is the one loan calculation with no closed-form solution. The amortization formula cannot be rearranged to isolate i, because the rate appears both as a multiplier and inside an exponent. It is therefore solved numerically: guess a rate, compute the payment it would produce, and adjust up or down until the computed payment matches the actual one. This is exactly how a lender derives the APR they must disclose, and it is why the figure is described as being "solved for" rather than calculated.
Solve M = P × [ i(1 + i)^n ] ÷ [ (1 + i)^n − 1 ] for i, by iterationAnnual rate = i × 12Simple check: Total interest = (M × n) − Pwhere:
Assumptions: Iterative methods converge quickly for conventional loans. If fees were deducted from the advance, use the net amount received as P and the answer becomes the APR rather than the note rate.
A dealer quotes a payment but not a rate. Work backwards to find it.
Result12.4% APR
Doing this on any quoted payment is the fastest way to detect an unfavourable deal. A dealer who leads with "only $404 a month" and omits the rate is relying on the payment sounding manageable; the derived 12.4% is the number that should drive the decision.