Finance
Interest Rate Calculator
Reverse-solve the interest rate on any loan from amount, monthly payment, and term. Uses bisection search for precision.
Loan details
Interest rate
7.420%
Total interest: $4,000
Monthly rate
0.6183%
Total paid
$24,000
Total interest
$4,000
Frequently Asked Questions about the Interest Rate Calculator
How does this calculator find the interest rate?
It uses bisection to solve the present-value equation for the monthly rate r: Loan = PMT x (1 - (1+r)^-n) / r. Given the loan amount, monthly payment, and term, there is exactly one rate that satisfies the equation, and the calculator converges on it in at most 200 iterations.
Why is there no closed-form formula?
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.
Can you give an example?
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%.
What if my payment is less than the principal divided by the term?
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.
Is this the APR or the nominal 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.