Work backwards from the payment to the rate you are really paying.
A dealer or lender quotes a monthly payment, not always the rate. Give this the loan amount, the payment and the term and it solves for the annual interest rate hidden inside that deal, so you can check whether the number you were told is honest.
Your loan
Enter the exact monthly payment you were quoted, principal and interest only. The number of payments is the term in months. This works for any fixed-rate, fully amortizing loan: auto, personal, or a fixed mortgage.
What the solved rate is telling you
How the payment maps to the rate
Payment vs implied rate
Where your total payments go
Every dollar you repay, split into the principal you borrowed and the interest the lender charges on top of it.
The numbers at a glance
Implied rate at different payment levels
Same loan amount and term. Only the monthly payment changes, so you can see how a higher payment (or a shorter term) points to a lower rate for the same amount borrowed.
| Monthly payment | Implied annual rate | Total interest | Total paid |
|---|
How interest rate is calculated
How to Calculate the Interest Rate on a Loan
Determining the interest rate from a known loan amount, monthly payment, and term requires solving the standard amortization formula in reverse. Since there is no closed-form solution, iterative methods like Newton-Raphson are used to converge on the annual rate. This calculator performs that computation instantly, showing both the APR and total cost of the loan.
Why Knowing Your Interest Rate Matters
Understanding the true interest rate on a loan helps you compare offers, evaluate refinancing opportunities, and make informed financial decisions. Even a small difference in rate, say 1%, can add up to thousands of dollars over the life of a loan. If you know only your payment and loan amount, this tool reveals the rate you are actually paying.
Interest Rate vs APR
The interest rate is the cost of borrowing the principal, while the Annual Percentage Rate (APR) includes the interest rate plus other fees and charges. When comparing loan offers, APR gives a more complete picture of the true cost. This calculator solves for the nominal annual rate based on your payment schedule.
Common questions
How is the interest rate calculated from my payment?
The calculator uses Newton's method to iteratively solve the amortization formula PMT = P × r(1+r)^n / ((1+r)^n - 1) for the monthly rate r. The annual rate is then r × 12 × 100. This numerical approach converges quickly to the precise rate.
Why can't I just divide total interest by the principal?
Simple division gives you the total interest percentage, not the annual rate. Loan interest compounds monthly, so the relationship between payment, principal, and rate is nonlinear. The amortization formula accounts for this compounding effect.
What if my payment is too low to cover the loan?
If your monthly payment multiplied by the number of months is less than or equal to the loan amount, the calculator will indicate that the payment is insufficient. You would need a higher payment or longer term to service the debt.
Does this work for all types of loans?
This calculator works for any fixed-rate, fully amortizing loan, including auto loans, personal loans, and fixed-rate mortgages. It does not apply to interest-only loans, adjustable-rate loans, or revolving credit like credit cards.
Estimates for planning only. This model assumes a fixed rate, a fully amortizing loan and equal monthly payments over the full term, so the solved rate reflects principal and interest alone. If your quoted payment folds in taxes, insurance or fees, the true note rate is lower than shown. Confirm the rate on your loan agreement before you rely on it.