How Is EMI Calculated? The Formula Explained With an Example
EMI stands for Equated Monthly Instalment: the fixed amount you pay every month until a loan is cleared. Banks quote it so confidently that it can look like magic, but it comes from one formula that you can check yourself. Here is how it works.
The formula
EMI = P × r × (1 + r)n ÷ ((1 + r)n − 1)
- P is the loan amount, also called the principal.
- r is the monthly interest rate. Divide the yearly rate by 12 and then by 100. A 9% yearly rate gives r = 9 ÷ 12 ÷ 100 = 0.0075.
- n is the number of monthly instalments. A 20-year loan has n = 240.
A full worked example
Suppose you borrow ₹10,00,000 at 9% a year for 20 years.
- P = ₹10,00,000, r = 0.0075, n = 240
- (1 + r)240 is about 6.0092
- EMI = 1,000,000 × 0.0075 × 6.0092 ÷ (6.0092 − 1) = about ₹8,997
Over 240 months you pay ₹8,997 × 240 = ₹21,59,342 in total. Subtract the ₹10,00,000 you borrowed and the interest cost is ₹11,59,342. In other words, over 20 years you pay more in interest than the amount you originally borrowed.
What each EMI is made of
Every EMI is the same amount, but its inside changes. Each month the bank charges interest on the balance still owed, and whatever is left of the EMI reduces the principal.
In month one, the interest is ₹10,00,000 × 0.0075 = ₹7,500. Out of an EMI of about ₹8,997, only about ₹1,497 goes to the principal. The following month the balance is a little lower, so the interest is a little lower and slightly more goes to principal. This continues until, near the end, almost the whole EMI is principal. This is why the early years of a long loan feel as if the balance barely moves.
How the three inputs change the EMI
| Loan | EMI | Total interest |
|---|---|---|
| ₹10,00,000 at 9% for 20 years | ₹8,997 | ₹11,59,342 |
| ₹10,00,000 at 9% for 15 years | ₹10,143 | ₹8,25,680 |
| ₹10,00,000 at 8.5% for 20 years | ₹8,678 | ₹10,82,776 |
A shorter tenure raises the monthly EMI but cuts the total interest sharply. A lower rate trims both. This trade-off is the core of every loan decision.
Reducing balance versus flat rate
The formula above assumes a reducing balance method, where interest is charged only on the amount still outstanding. This is how home loans and most bank loans work. Some lenders quote a flat rate, where interest is charged on the full original amount for the whole tenure. A flat rate of 8% is much more expensive than a reducing rate of 8%, because you are paying interest on money you have already repaid. When you compare offers, convert them to the same basis or ask for the effective annual rate.
Things the EMI does not include
- Processing fees, which are usually a percentage of the loan.
- Insurance premiums that some lenders bundle in.
- Prepayment or foreclosure charges, where they apply.
- Rate changes on floating-rate loans, which change the EMI or the tenure.
Check any quote yourself
Before you sign, enter the amount, rate and tenure in our EMI Calculator. It gives the monthly EMI, the total interest and a month-by-month schedule so you can see exactly how much of each payment is principal. If the number from the lender is far from the calculator, ask what extra charges are included. For ideas on cutting the cost of a loan, read How to Reduce Your EMI and Total Interest.
This is general information, not financial advice. Loan terms differ between lenders, so confirm the figures with your bank.