How is EMI calculated? The formula, explained with examples

What an EMI is

EMI stands for equated monthly instalment: the same amount paid every month until a loan is repaid. Almost every retail loan in India — home, car, bike, personal and education loans — is repaid this way.

Although the EMI stays the same, what it pays for changes every month. Part of each EMI pays the interest due for that month; the rest reduces the principal. Because the principal keeps falling, next month’s interest is a little lower, so a little more of the same EMI goes to principal. This is called a reducing-balance (or diminishing-balance) loan.

The EMI formula

Banks use one formula for every reducing-balance loan: EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1).

• P is the principal — the amount you borrow.
• r is the monthly interest rate: the annual rate divided by 12 and by 100. At 9% a year, r = 9 ÷ 12 ÷ 100 = 0.0075.
• n is the number of monthly instalments: 10 years is 120 months.

The formula finds the single monthly payment that, after interest is charged on the falling balance each month, brings the balance to exactly zero after n payments.

Worked example: ₹10 lakh at 9% for 10 years

With P = 10,00,000, r = 0.0075 and n = 120, (1 + r)ⁿ = 1.0075¹²⁰ ≈ 2.4514. The EMI is 10,00,000 × 0.0075 × 2.4514 ÷ 1.4514 ≈ ₹12,668. Over 120 months you repay ₹15.2 lakh — ₹5.2 lakh of it interest.

Here is how the first few EMIs split between interest and principal:

Month one’s interest is simply the full ₹10 lakh × 0.0075 = ₹7,500. The rest of the ₹12,668 EMI, ₹5,168, reduces the loan. By month 60 — halfway through the tenure — you still owe ₹6.1 lakh, because the early EMIs were mostly interest. The final EMI is almost entirely principal.

Reading an amortisation schedule

An amortisation schedule lists every EMI with its interest part, principal part and the balance left afterwards. Summarised by year, the same loan looks like this:

Two practical lessons follow. First, a prepayment early in the loan saves far more interest than the same prepayment late in the loan, because it removes principal that would otherwise attract interest for many years. Second, the principal you repay rises each year — useful to know for home loans, where principal counts towards Section 80C and interest towards Section 24(b).

What changes your EMI

• Loan amount: the EMI rises in direct proportion. Borrowing 10% more means an EMI 10% higher.
• Interest rate: a higher rate raises the EMI, and the effect is larger on long loans. On a 20-year home loan, each 0.5% adds roughly 3%–4% to the EMI.
• Tenure: a longer tenure lowers the EMI but increases total interest, often steeply. Doubling a 10-year loan to 20 years does not halve the EMI — at 9% it falls by less than a third, while total interest more than doubles.

Why your bank’s figure may differ by a few rupees

Lenders round EMIs differently, count interest from the actual disbursement date, and may charge “broken-period” or pre-EMI interest for the days between disbursement and the first EMI cycle. The difference is usually small and appears in the first instalment. A home loan disbursed in stages for an under-construction flat charges pre-EMI interest on the amount released until full EMIs begin.

Flat-rate loans are different

Some dealer-arranged car, bike and consumer loans charge a “flat” rate: interest on the original amount for the whole tenure, ignoring repayments. The EMI formula above does not apply, and the real cost is far higher than the quoted number suggests. See our guide to flat and reducing interest rates.

Frequently asked questions