Work out the interest rate (APR) from a loan amount, monthly payment and term.
How interest rate is worked out
If you know the loan amount, the monthly payment and the term but not the rate, this calculator solves for it. It finds the rate that makes the payments match the loan.
Handy for reverse-engineering a quoted deal or checking an offer.
Try it with these numbers
Worked through, a loan amount of 20,000 produces a interest rate of 7.42%. Underneath, Monthly rate comes out at 0.6183% and Total interest at $4,000. Change any field and every figure updates as you type.
How to use it
- Enter the loan amount.
- Enter the monthly payment and term in months.
- Read the implied APR.
The maths behind it
solves for the rate r where
loan = payment × (1 − (1+r)⁻ⁿ) ÷ r
Common questions
Can I find the rate from the payment?
Yes — with the amount, payment and term, the rate is the only unknown, and the calculator solves for it numerically.
Why isn’t there a simple formula?
The rate can’t be isolated algebraically in the payment equation, so it’s found by iteration.
Is this the APR?
It’s the periodic rate annualized. A lender’s stated APR may differ slightly if fees are included.