Solve for the interest rate given principal, payment, and term of any loan.
Enter the amount borrowed, the fixed monthly payment and the number of payments (in months or years). The calculator works backwards to find the interest rate built into that loan.
This is handy for checking a dealer or store financing offer that only quotes a monthly payment. The result is the APR implied by the payments alone — it does not include fees that are paid separately.
M = P × r / (1 − (1 + r)^−n)There is no closed-form solution for r, so the calculator solves it numerically by bisection (the payment rises steadily as the rate rises, so the search always converges). APR = r × 12; effective annual rate = (1 + r)^12 − 1.
Enter the loan amount, the monthly payment and the number of payments. Because the loan payment formula cannot be rearranged for the rate, the calculator tries rates until the computed payment matches yours to a fraction of a cent.
APR is the monthly rate multiplied by 12. The effective annual rate (or APY) also accounts for interest compounding monthly, so it is slightly higher: a 12% APR is about a 12.68% effective rate.
Sellers often advertise a monthly payment rather than a rate. Solving for the rate lets you compare that offer fairly against a bank or credit-union loan.
If the payments add up to less than the amount borrowed, the implied rate would be negative, which is not a real loan. Check the payment, term and loan amount.
The nominal interest rate is the base rate charged on a loan. The APR adds in fees, points, and other charges to show the true annual cost of borrowing. When comparing loan offers, always use APR for an apples-to-apples comparison. Mortgage APR may be higher than the quoted rate due to origination fees, discount points, and closing costs.
Did you know?
The Federal Reserve has changed its benchmark interest rate over 100 times since 1990. The federal funds rate hit a historic low of 0–0.25% during both the 2008 financial crisis and the 2020 COVID-19 pandemic.
Interest rates have been regulated since ancient times. The Code of Hammurabi (1754 BCE) set maximum rates at 20% for silver and 33% for grain loans. Usury laws limiting interest rates existed in medieval Europe, often tied to religious prohibitions. Modern central banking, which manages interest rates to control economic activity, began with the Bank of England in 1694.
APR (Annual Percentage Rate) includes fees and points, making it a more accurate measure of loan cost than the nominal interest rate alone.
A 1% difference in interest rate on a $300,000 30-year mortgage changes the monthly payment by approximately $180 and total interest by over $64,000.
Central banks worldwide control short-term interest rates, which cascade through the economy affecting mortgages, savings, car loans, and credit cards.