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 solves the standard loan equation for r using bisection: PMT = L x (r x (1+r)^n) / ((1+r)^n - 1). Given loan amount, monthly payment, and term, there is exactly one rate that fits.
Why is there no closed-form formula?
The amortization equation is non-linear in r and cannot be rearranged algebraically. Every financial calculator (including HP, TI, and Excel RATE) uses iteration: bisection or Newton-Raphson.
Can you give an example?
A $20,000 loan paid off with $400 per month over 5 years implies an annual rate of about 7.42%. Drop the payment to $380 over the same term and the implied rate is roughly 5.36%.
What if my payment is less than the principal divided by the term?
The loan would never be repaid, so no positive rate exists. The calculator returns no result. Increase 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 based on a 12-month compounding convention. APR also includes fees, which this calculator does not see. Use the APR calculator if you want to include origination or closing fees.