How a loan EMI is actually calculated
EMI stands for Equated Monthly Instalment — the fixed amount you pay every month until a loan is cleared. It looks like a single mysterious number in an app, but it comes from one formula that anyone can follow. Here it is, with a full worked example.
The idea behind the formula
An EMI is "equated" because every monthly payment is identical, even though the split between interest and principal changes over time. Early on, most of each payment is interest on a large outstanding balance; later, as the balance shrinks, more of each payment goes to principal. The formula finds the single monthly amount that pays off both the borrowed money and all the interest exactly over the chosen number of months.
The formula
where:
- P = the principal — the amount you borrow.
- r = the monthly interest rate as a decimal. If the bank quotes an annual rate, divide by 12 and by 100. A 9% annual rate gives r = 9 ÷ 12 ÷ 100 = 0.0075.
- n = the tenure in months. A 20-year loan is n = 240.
The term (1 + r)n is simply the monthly rate compounded over every month of the loan. That one quantity appears twice; compute it once and the rest is arithmetic.
A worked example: ₹10,00,000 at 9% for 20 years
Take a home loan of ten lakh rupees at 9% per year, repaid over 20 years.
| Quantity | Value |
|---|---|
| Principal, P | ₹10,00,000 |
| Monthly rate, r | 9 ÷ 12 ÷ 100 = 0.0075 |
| Months, n | 240 |
| (1 + r)n = 1.0075240 | ≈ 6.009 |
Put those into the formula:
= 7500 × 6.009 ÷ 5.009
≈ ₹8,997 per month
Over the full term you pay 8,997 × 240 ≈ ₹21,59,000. Since you borrowed ₹10,00,000, the interest over 20 years is about ₹11,59,000 — more than the loan itself. That is the thing most people find surprising, and it's why the tenure matters so much.
What moves the EMI
- A higher rate raises both the interest and the EMI. At 10% instead of 9%, the same loan costs roughly ₹9,650 a month.
- A longer tenure lowers the monthly EMI but increases total interest — you pay a smaller amount for far longer. Stretching this loan to 25 years drops the EMI to about ₹8,392 but pushes total interest well past ₹15 lakh.
- A larger principal scales the EMI proportionally: double the loan, double the instalment, if rate and tenure are unchanged.
Where prepayment fits
Because so much of the early interest rides on a large outstanding balance, paying extra in the first years is disproportionately powerful. A prepayment reduces the principal directly, and every rupee of principal removed early saves all the future interest it would have attracted. This is why a modest annual prepayment can cut years off a long loan — and why a good calculator lets you model it rather than guess.
You can run any of these numbers for your own loan, including prepayment and a full amortisation schedule, in Northcell's EMI Calculator — offline, with exact arithmetic.