Finance
Find the annual interest rate from loan amount, monthly payment, and term.
Annual Interest Rate
5.28%per year
Calculated using the monthly rate that satisfies your loan payment equation.
An interest rate calculator is a financial tool that reverse-engineers the annual interest rate from three loan parameters: principal (loan amount), monthly payment, and loan term (in months). Instead of starting with a rate and computing the payment, you start with the payment and discover what rate it implies. This is crucial for evaluating loan offers, comparing lenders, or understanding the true cost of your existing debt.
The calculator uses the EMI (Equated Monthly Installment) equation—the same formula banks use to calculate your payment—and solves it in reverse. Given the loan amount, payment, and months, it uses numerical methods (bisection search) to find the monthly interest rate that satisfies the equation. Once the monthly rate is found, it multiplies by 12 and by 100 to convert to an annual percentage. The calculator also computes total paid and total interest, showing you the true cost of borrowing at that rate.
Payment = Principal × r(1+r)^n / ((1+r)^n − 1); solve for r; Annual Rate = r × 1200 (as percentage)The EMI formula expresses your fixed monthly payment in terms of principal, monthly interest rate r, and number of months n. The calculator iteratively searches for the monthly rate r that makes this equation true for your specific payment. Once found, multiplying by 12 and by 100 yields the annual interest rate as a percentage.
| Input | Result | Notes |
|---|---|---|
| Loan: $20,000 | Payment: $380/month | Term: 60 months | Annual Rate: ~10.76% | Total Paid: $22,800 | Total Interest: $2,800 | A typical personal loan. The hidden interest rate is revealed; compare this to other offers to choose the best deal. |
| Loan: €50,000 | Payment: €900/month | Term: 84 months | Annual Rate: ~4.89% | Total Paid: €75,600 | Total Interest: €25,600 | A car loan. The 4.89% rate is competitive; total interest of €25,600 shows the true cost over 7 years. |
| Loan: £100,000 | Payment: £1,200/month | Term: 120 months | Annual Rate: ~3.88% | Total Paid: £144,000 | Total Interest: £44,000 | A mortgage-like rate. The rate is low, so most early payments are interest, but long terms accumulate large total interest. |
APR (Annual Percentage Rate) includes fees, insurance, and other costs beyond interest, rolled into an annualized rate for comparison. This calculator returns the pure interest rate implied by your payment—it excludes external fees. The calculator's result is close to APR if no fees are bundled into the payment.
If the quoted rate and your calculated rate differ, the gap usually means fees or charges are rolled into your payment. Origination fees, insurance, servicing fees, or property taxes bundled into a mortgage payment will inflate the apparent interest rate when you solve backward. Ask your lender to itemize your payment.
Credit cards rarely have fixed terms or fixed payments—balances and rates fluctuate. This calculator assumes a fixed payment and fixed rate over a set term, so it's not suitable for credit cards. For fixed-rate installment debt (personal loans, car loans, mortgages), it works perfectly.
This typically means the monthly payment is too low to ever pay off the principal in the given term at any reasonable interest rate, or the term is impossibly short. Verify that your payment is at least the principal divided by the number of months (ignoring interest).
Yes, absolutely. Calculate the implied rate for each offer using the same principal and term. The offer with the lowest calculated rate is the cheapest in pure interest terms—but always compare APRs and total fees to lenders' quotes.
The calculator uses a numerical bisection method that converges to the true rate within 0.01% accuracy. This is more than sufficient for loan comparison and verification; it matches lender calculators and financial software.