The EMI formula
For a fixed-rate loan repaid in equal monthly instalments, the EMI is:
EMI = P × i × (1 + i)^n ÷ [(1 + i)^n − 1]
Here P is the loan amount, i is the monthly interest rate (annual rate ÷ 12 ÷ 100) and n is the number of monthly payments. If the interest rate is zero, the EMI is simply P ÷ n.
A worked example
Borrow 1,000,000 at 9% a year for 10 years (120 months). The monthly rate is 9/12/100 = 0.0075. Putting the numbers into the formula gives an EMI of 12,667.58. Over 120 payments you repay 1,520,109.29, so the total interest is 520,109.29 — about 52% of the amount borrowed. You can check these figures with the EMI Calculator.
Where each payment goes
Every EMI is split between interest and principal. In the first month the interest is the full balance times the monthly rate: 1,000,000.00 × 0.0075 = 7,500.00. The rest of the EMI, 5,167.58, reduces the principal. Because the balance shrinks, the interest portion falls every month and the principal portion grows, so the last payments are almost all principal. This is why early repayment saves more than late repayment.
How tenure and rate change the cost
A longer tenure lowers the monthly EMI but raises the total interest. For a 1,000,000 loan at 9%:
| Tenure | EMI | Total interest |
|---|---|---|
| 5 years | 20,758.36 | 245,501.31 |
| 10 years | 12,667.58 | 520,109.29 |
| 15 years | 10,142.67 | 825,679.85 |
| 20 years | 8,997.26 | 1,159,342.29 |
The interest rate matters just as much. For the same loan over 10 years:
| Annual rate | EMI | Total interest |
|---|---|---|
| 8% | 12,132.76 | 455,931.13 |
| 9% | 12,667.58 | 520,109.29 |
| 10% | 13,215.07 | 585,808.84 |
| 11% | 13,775.00 | 653,000.14 |
Even a one-point difference in rate changes the total cost noticeably, so compare offers on the total amount repaid, not only the EMI.
What a prepayment does
Paying extra towards the principal reduces future interest. In the example above, a one-off prepayment of 100,000 after the 12th EMI, with the EMI kept the same, finishes the loan in 104 months instead of 120 and cuts the total paid by about 211,218.50. Check your lender's prepayment rules first, as some charge a fee or apply the extra amount differently.
What the formula leaves out
The standard formula assumes a fixed rate and equal monthly periods. It does not include processing fees, insurance, taxes, rate changes on floating-rate loans, or the way a lender counts days and rounds amounts. That is why a lender's schedule can differ slightly from a calculator. Treat the calculator as a clear estimate and confirm the final figures in your loan agreement.
Try it with your own numbers
Use the EMI Calculator, the Home Loan EMI Calculator or the Car Loan EMI Calculator to see your own instalment, total interest and amount paid.
Frequently asked questions
Is the EMI the same for the whole loan?
On a fixed-rate loan, yes. On a floating-rate loan the lender may change the EMI or the tenure when the rate changes.
Does a longer tenure save money?
It lowers the monthly EMI but increases the total interest paid, because you owe a balance for more months.
Why does my lender's EMI differ slightly from a calculator?
Lenders may round differently, count days instead of whole months, or add fees and insurance that the basic formula excludes.
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