About the interest rate calculator
Sometimes you know what a loan costs each month but not the rate behind it. This calculator finds the annual interest rate (APR) that makes the loan amount, the term and the monthly payment fit together.
The payment formula cannot be solved for the rate directly, so the calculator uses a numerical search (Newton’s method backed by bisection) that converges to the rate within a tiny fraction of a cent. If the payment would not even repay the loan, or the rate would be absurdly high, you get a message explaining what to change.
Formula
- Find r such that Payment = L × r ÷ (1 − (1 + r)^−n)
- r = monthly rate, n = number of months, L = loan amount
- APR = r × 12
Example
A $200,000 loan over 30 years with a $1,199.10 monthly payment has an interest rate of 6.000%.