EMI Calculator formula — how it actually works

The EMI formula looks intimidating, but it only does one sensible thing: it finds the fixed monthly payment that repays the loan exactly, with interest, by the final month. Written out, EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the amount borrowed, r is the monthly interest rate and n is the number of monthly payments.

Where r and n come from

Lenders quote an annual rate, so r is that rate divided by 1,200 — by 12 for the months, and by 100 for the percentage. A 10% annual rate becomes a monthly rate of 0.8333%. And n is the tenure in months: 20 years is 240 payments. Those two conversions are the most common source of wrong answers when people try the formula themselves.

Why the power term is there

Each month you owe interest on the remaining balance, and each payment shrinks that balance. The (1 + r)^n term is compound interest running forward over the whole loan, and dividing by ((1 + r)^n − 1) spreads the total back into equal monthly slices. Without it, you would be guessing at a payment that leaves a balance at the end.

Worked example

Borrow ₹10,00,000 at 10% for 20 years: r = 0.008333 and n = 240, giving an EMI of ₹9,650. In the first month, interest alone is ₹8,333 of that payment, so only ₹1,317 reduces the loan. By the final year the split has flipped, and almost the whole payment goes to principal. The EMI never changes — only the split does.

Frequently asked questions

What if the interest rate is 0%?

The formula divides by zero, so the calculator handles it separately: the EMI is simply the amount divided by the number of months.

Does the formula include fees?

No. Processing fees, insurance and late charges sit outside the formula, so a lender’s schedule can differ slightly from the calculator.

Is this a flat-rate calculation?

No, it is a reducing-balance calculation. Interest is charged on what you still owe, which is how most housing and personal loans actually work.