A worked example: ₹5L loan, ₹15,000 EMI, 4 years
A ₹5,00,000 loan repaid at ₹15,000 a month over 48 months implies an annual interest rate of 19.19% — a figure nowhere in the original inputs, only recoverable by working backward from them.
Why this can't be solved directly, only narrowed in on
The standard EMI formula (P = EMI × [(1+r)ⁿ−1] ÷ [r×(1+r)ⁿ]) has no algebraic way to isolate r on one side — so instead of solving for it directly, the calculator tries a rate, checks whether it reproduces the known principal, and repeatedly narrows the range (bisection) until the guess is accurate to a tiny fraction of a percent.
A smaller loan, a smaller implied rate: ₹2L, ₹6,500 EMI, 3 years
A ₹2,00,000 loan repaid at ₹6,500 a month over 36 months implies a lower annual rate of 10.49% — a smaller EMI relative to the loan amount over a similar timeframe corresponds to a gentler interest rate.
Why this matters for comparing loan offers
Some lenders advertise an EMI per lakh borrowed rather than a headline interest rate, making offers hard to compare directly. Reverse-engineering the actual rate from the quoted EMI, principal, and tenure puts every offer on the same footing, regardless of how it was originally presented.
When the numbers don't produce a valid rate
The EMI multiplied by the tenure must exceed the principal for any positive interest rate to exist — if the total repaid barely covers (or falls short of) the amount borrowed, the inputs are inconsistent with a real interest-bearing loan and should be double-checked.