Interest Rate Calculator
Free interest rate calculator. Solve the annual APR on any amortizing loan from loan amount, term, and monthly payment. Includes effective APY, term sensitivity, and Excel export.
Frequently asked questions
How do you calculate the interest rate on a loan from the payment?
You solve the amortization equation M = P·r·(1+r)ⁿ / ((1+r)ⁿ − 1) for the monthly rate r, given loan amount P, monthly payment M, and term n. There is no closed-form solution, so numerical methods like bisection or Newton-Raphson are used. This calculator uses bisection because it always converges when a solution exists.
What is the difference between interest rate and APR?
The interest rate is the pure cost of borrowing on the loan balance. APR (Annual Percentage Rate) folds in origination fees and other required loan costs, so it is always ≥ the stated rate. This calculator solves the pure interest rate from the payment. To include fees, use the Personal Loan Calculator, which reports both the nominal rate and the effective APR.
What is the effective APY on a loan?
Effective APY is (1 + r_monthly)¹² − 1, where r_monthly is the monthly rate. It reflects how much you would pay annually if interest compounded monthly on the outstanding balance. On a 6% APR loan with monthly compounding, the effective APY is about 6.168%.
Why does the calculator say "payment too low"?
If the total of all payments (M × n) is less than or equal to the loan amount P, no positive interest rate can solve the loan — the payments do not even return the principal. This is the zero-rate boundary: raise the payment above P ÷ n to imply a real interest rate.
When would I use this calculator?
When a lender, dealer, or seller quotes you a monthly payment and term but hides or refuses to disclose the actual interest rate — common in auto financing, seller financing, and buy-here-pay-here deals. Enter the numbers and reverse-engineer the effective rate to compare against fair market benchmarks.
Does the term sensitivity table assume the payment stays the same?
Yes. The table shows what interest rate would be implied if you kept the same loan amount and monthly payment but changed the term. A longer term with the same payment implies a lower rate — but you pay far more total interest because you pay for longer.