How EMI Is Calculated
An EMI (Equated Monthly Installment) is the fixed amount you pay every month until a loan is cleared. The amount never changes, but what it is made of does: early payments are mostly interest, and later payments are mostly principal. Understanding that split is what lets you judge a loan offer, a longer tenure or a prepayment properly.
The EMI formula
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, then by 100. A 9% annual rate gives r = 9 ÷ 12 ÷ 100 = 0.0075.
- n is the number of monthly payments: tenure in years × 12.
The formula comes from requiring that the present value of all n equal payments, discounted at the monthly rate, equals the amount borrowed. If the interest rate is 0%, it collapses to P ÷ n.
A worked example
Take a loan of ₹10,00,000 at 9% a year for 20 years. Here P = 10,00,000, r = 0.0075 and n = 240. First, (1.0075)^240 ≈ 6.0092. Then:
EMI = 10,00,000 × 0.0075 × 6.0092 ÷ (6.0092 − 1) ≈ ₹8,997 per month.
Over 240 months that adds up to about ₹21,59,342, so you repay roughly ₹11,59,342 in interest on a ₹10,00,000 loan. The interest is more than the amount you borrowed, which surprises many first-time borrowers.
How each payment is split
Each month, interest is charged on the balance still outstanding. Whatever is left of the EMI after interest reduces the principal. Using the unrounded EMI of ₹8,997.26, the schedule begins like this:
| Month | Interest | Principal repaid | Balance after payment |
|---|---|---|---|
| 1 | ₹7,500.00 | ₹1,497.26 | ₹9,98,502.74 |
| 2 | ₹7,488.77 | ₹1,508.49 | ₹9,96,994.25 |
| 3 | ₹7,477.46 | ₹1,519.80 | ₹9,95,474.45 |
| 240 | ₹66.98 | ₹8,930.28 | ₹0 |
In month 1, about 83% of your EMI is interest. By month 240 it is under 1%. Real lenders round each instalment to the nearest rupee, so the final instalment can differ from the others by a few rupees.
How rate and tenure change the numbers
The table below shows ₹10,00,000 borrowed under different terms.
| Rate | Tenure | EMI | Total interest |
|---|---|---|---|
| 9% | 10 years | ₹12,668 | ₹5,20,109 |
| 9% | 15 years | ₹10,143 | ₹8,25,680 |
| 9% | 20 years | ₹8,997 | ₹11,59,342 |
| 9% | 30 years | ₹8,046 | ₹18,96,641 |
| 8% | 20 years | ₹8,364 | ₹10,07,456 |
| 10% | 20 years | ₹9,650 | ₹13,16,052 |
| 11% | 20 years | ₹10,322 | ₹14,77,252 |
Stretching from 20 to 30 years cuts the EMI by only about ₹950 a month but adds roughly ₹7.4 lakh of interest. Going from 20 to 15 years raises the EMI by about ₹1,146 and saves about ₹3.3 lakh. Each extra percentage point on the rate adds roughly ₹630–670 a month at this size and tenure.
Reducing balance vs flat rate
Home, car and most personal loans use the reducing-balance method, which is what the formula above assumes: interest is recalculated each month on what you still owe. Some lenders quote a flat rate, where interest is charged on the original principal for the whole tenure. A 9% flat rate on ₹10,00,000 for 20 years means ₹18,00,000 of interest and an EMI of ₹11,667. That is equivalent to a reducing-balance rate of about 12.9%. When comparing offers, convert flat rates to reducing-balance equivalents, or ask the lender for the effective rate.
Prepayment
Because interest is charged on the outstanding balance, any extra payment goes straight to principal and reduces all future interest. On the example loan, a one-time prepayment of ₹1,00,000 after 5 years, with the EMI kept the same, ends the loan after about 203 months instead of 240 and cuts interest from about ₹11.59 lakh to about ₹9.25 lakh. Prepaying early matters far more than prepaying late, since the early balance is largest. Check your loan agreement first, as some lenders charge prepayment fees, particularly on fixed-rate loans, and rules differ by lender, loan type and country.
Using the calculator
The EMI calculator takes the loan amount, annual rate and tenure in years, and shows the monthly EMI, total interest and total payable. It does not produce a month-by-month schedule, so use the formula above if you need the split for a particular month. The figures are estimates: actual EMIs depend on how your lender rounds, when the first instalment falls, any processing fees, and whether your rate is floating and resets over time.