Interest Rate Calculator

It uses bisection to solve the present-value equation for the monthly rate r: Loan = PMT x (1 - (1+r)^-n) / r. Given a payment schedule that fully repays the loan, there is one nonnegative rate that satisfies the equation. The calculator brackets that root and narrows the interval until the present-value residual or the floating-point interval reaches its tolerance.

The present-value equation is non-linear in r and cannot be rearranged algebraically to isolate it. Every financial tool (from HP and TI calculators to Excel's RATE function) uses numerical iteration such as bisection or Newton-Raphson for the same reason.

A $20,000 loan repaid with $400 per month over 5 years implies an annual rate of about 7.42%. Drop the payment to $380 per month over the same 5-year term and the implied rate falls to roughly 5.28%.

The total amount you would pay is less than what you borrowed, which means no positive interest rate can produce that result. The calculator returns no answer. Raise the monthly payment or shorten the term to find a valid rate.

It is the nominal annual rate, calculated as monthly rate x 12. APR also factors in origination fees, points, and closing costs, which this calculator does not see. If you need to include fees, use a dedicated APR calculator.