How Is EMI Calculated? The Formula, Explained with an Example
A step-by-step walkthrough of the EMI formula, how each payment splits into interest and principal, and why the first years of a loan are mostly interest.
An Equated Monthly Installment (EMI) is the fixed amount you pay your lender every month until a loan is fully repaid. It looks like a single number, but it hides a precise piece of mathematics that decides how much interest you pay and how fast your debt shrinks. Once you understand the formula, you can estimate any loan in seconds and spot offers that do not add up.
1. The EMI Formula
For a standard reducing-balance loan, the EMI is calculated as:
- P is the principal, the amount you borrow.
- r is the monthly interest rate. Divide the annual rate by 12 and by 100. An annual rate of 9% becomes 9 ÷ 12 ÷ 100 = 0.0075.
- n is the number of monthly instalments. A five-year loan has n = 60.
The formula works because it finds the single fixed payment that, when each month's interest is charged on the remaining balance, brings the balance to exactly zero after n payments.
2. A Worked Example
Suppose you borrow ₹10,00,000 at 9% per annum for 5 years. Here P = 10,00,000, r = 0.0075 and n = 60.
• Monthly EMI: ₹20,758
• Total repayment: ₹20,758 × 60 = ₹12,45,501 (approximately)
• Total interest paid: ₹2,45,501
You can reproduce this instantly with the calculator on our home page by entering the same three inputs; the result will match the figures above.
3. How Each EMI Splits into Interest and Principal
Every EMI contains two parts. The interest part is the monthly rate multiplied by the balance outstanding at the start of that month. The remainder of the EMI repays principal. Because the balance shrinks every month, the interest part falls and the principal part grows, even though the EMI itself never changes.
| Month | Interest | Principal | Balance After Payment |
|---|---|---|---|
| 1 | ₹7,500 | ₹13,258 | ₹9,86,742 |
| 2 | ₹7,401 | ₹13,358 | ₹9,73,384 |
| 3 | ₹7,300 | ₹13,458 | ₹9,59,926 |
| 60 | ₹155 | ₹20,603 | ₹0 |
This full table for every month is what lenders call an amortization schedule, and our calculator generates it for you in yearly and monthly views.
4. What Changes the EMI the Most
- Principal: The EMI grows in direct proportion to the amount borrowed. Doubling the loan doubles the EMI.
- Interest rate: Even a 1% rise in the rate lifts the EMI noticeably, and the effect compounds over long tenures.
- Tenure: A longer tenure lowers the EMI but raises the total interest, often dramatically. The next guide on choosing a tenure shows the numbers.
5. Charges the Formula Does Not Include
The formula covers only interest and principal. Processing fees, documentation charges, loan-related insurance, GST on fees and, for credit card EMIs, GST on interest are charged separately. These can add up to 1% to 3% of the loan amount, so always compare lenders on the total cost of the loan rather than on the EMI alone.
6. Quick Sanity Checks
- Multiply the EMI by the number of months. If the result is less than the amount you borrowed, something is wrong.
- For a rough estimate at typical rates, a 20-year loan costs a little under ₹900 per month for every ₹1,00,000 borrowed at about 8.75%.
- If a lender's quoted EMI is lower than the formula result for the stated rate, the quoted rate is probably a flat rate or the tenure is different from what you assumed.