Interest Rate Calculator
Annual interest rate (%) from loan amount, monthly payment and term.
How it works
Solve for monthly r where P×r ÷ (1−(1+r)^−n) = payment; annual = r×12×100%
Solved numerically by bisection (no closed form). No solution if the payment cannot cover the principal.
Worked example
Loan 100,000 over 36 months at 3,000/month, solving backwards:
100000 = 3000 × (1 − (1+r)⁻³⁶) ÷ r gives r ≈ 0.42%/month, about 5.2% a year.
Notes and limitations
The true annualised cost (IRR) of an amortized loan usually exceeds the nominal rate because principal declines monthly. Compare loans on IRR/APR; upfront fees raise the real rate materially.