The formula
How it works
Work backwards from a loan’s payment to the interest rate behind it. Enter the amount borrowed, the monthly payment and the number of payments, and the calculator finds the rate you are actually being charged.
FAQ
Why work out the rate from the payment?
Some offers quote only a monthly payment and a term, not the interest rate. Recovering the rate lets you compare deals fairly and spot when a “low payment” hides a high rate stretched over a long term.
Is this the APR?
This is the interest rate implied by the payments alone. A true APR also folds in fees and charges, so it can be a little higher than the rate shown here if the loan has upfront costs.
What does “no solution” mean?
It means the monthly payment you entered, multiplied by the number of payments, does not even cover the loan amount. There is no positive interest rate that produces a payment that low, so the calculator has nothing valid to solve for.
How does the loan term affect the rate found?
For the same payment and loan amount, a longer term implies a lower rate, since more payments are being applied to the same principal. Stretching the term is often how lenders advertise a smaller monthly payment while charging a similar or higher rate overall.
Can I use this to check a rate a lender already quoted?
Yes — plug in the loan amount, the payment you were quoted, and the term, and compare the rate the calculator finds against the rate the lender stated. A mismatch can point to fees baked into the payment or a misquoted term.
Why does the calculator need to solve numerically instead of computing the rate directly?
The loan payment formula cannot be rearranged algebraically to isolate the rate, since it appears both inside and outside an exponent. Instead, the calculator tries successive rates and narrows in on the one that reproduces your payment.
Does the number of payments have to be in months?
The calculator treats the term as monthly payments and returns a monthly rate scaled to an annual figure. If your loan pays on a different schedule, convert the term and payment count to a monthly-equivalent basis first.
About the interest rate calculator
This calculator finds the interest rate on a loan when you know the amount borrowed, the monthly payment and how many payments there are. Lenders sometimes advertise a loan by its monthly payment rather than its rate, which makes deals hard to compare. By reversing the usual loan calculation, this tool recovers the hidden rate, so you can see exactly how expensive the borrowing really is.
How to use it
Enter the loan amount, the fixed monthly payment, and the total number of monthly payments. The calculator returns the annual interest rate that produces that payment. For example, borrowing $20,000 with a $396 monthly payment over 60 months works out to about a 7% annual rate. If the payments add up to no more than you borrowed, the implied rate is zero — an interest-free deal.
The formula
The loan payment formula, , links the payment , the amount , the monthly rate and the number of payments . There is no simple way to rearrange it to isolate , so the calculator solves it numerically — trying rates and narrowing in until the formula matches your payment. Multiplying the monthly rate it finds by 12 gives the annual rate.
Where it is used
Borrowers use it to uncover the rate behind a payment-only offer, whether on a car, a personal loan or store finance, and to check a rate a lender has quoted. It is handy for comparing a low monthly payment over a long term against a higher payment over a short one. The same reverse calculation underlies APR figures and the disclosures lenders are required to provide.