How EMI Is Calculated: Formula, Examples and Prepayment
EMI is calculated with the formula EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the loan amount, r is the monthly interest rate (the annual rate ÷ 12 ÷ 100) and n is the number of monthly instalments. For a ₹50 lakh home loan at 8.5% for 20 years, that gives an EMI of ₹43,391. This guide walks through the formula step by step, shows worked examples for home, car and personal loans, explains why your early EMIs are mostly interest, and shows how prepaying cuts the total you pay.
The EMI formula, step by step
EMI stands for equated monthly instalment: the same amount every month, which covers that month's interest and pays back part of the loan. Indian banks work it out on a monthly reducing balance, which means interest is charged each month only on the amount you still owe.
- P is the principal, the amount you borrow.
- r is the monthly interest rate: the annual rate divided by 12, then by 100. At 8.5% a year, r = 8.5 ÷ 12 ÷ 100 = 0.0070833.
- n is the number of months: 20 years is 240 months.
Here is the ₹50,00,000 home loan at 8.5% for 20 years worked through:
- Work out (1 + r)^n: 1.0070833 raised to the power 240 is about 5.4412.
- Multiply P × r × (1 + r)^n: 50,00,000 × 0.0070833 × 5.4412 is about 1,92,711.
- Divide by (1 + r)^n − 1, which is 4.4412: 1,92,711 ÷ 4.4412 is about 43,391.
- So the EMI is ₹43,391 a month. Over 240 months you repay about ₹1,04,13,879, of which ₹54,13,879 is interest.
You do not need to do this by hand. The calculators below do it as you type and show the full schedule.
Worked examples: home, car and personal loans
These are the examples our calculators open with. The rates are only examples, not offers; use the rate your lender quotes.
| Loan | Amount, rate, tenure | EMI | Total interest |
|---|---|---|---|
| Home loan | ₹50,00,000 at 8.5% for 20 years | ₹43,391 | ₹54,13,879 |
| Car loan | ₹8,00,000 at 9.5% for 5 years | ₹16,801 | about ₹2,08,089 |
| Personal loan | ₹3,00,000 at 12% for 3 years | ₹9,964 | about ₹58,715 |
Notice how much the tenure matters. On the home loan, the interest is more than the loan itself, because it runs for 20 years. Stretching it to 25 years lowers the EMI to about ₹40,261, but the total interest rises to about ₹71 lakh.
Why your early EMIs are mostly interest
Each month the bank first takes the interest on what you still owe, and the rest of the EMI reduces the loan. At the start you owe the most, so most of the EMI goes on interest.
| ₹50 lakh at 8.5% for 20 years | Interest | Principal repaid |
|---|---|---|
| First EMI of ₹43,391 | ₹35,417 | ₹7,974 |
| First year (12 EMIs) | about ₹4,21,182 | about ₹99,511 |
In the first year you pay over ₹5.2 lakh in EMIs but the loan goes down by less than ₹1 lakh. Only after about 166 EMIs, almost 14 years into the 20, have you repaid half the loan. As the balance falls, the interest part shrinks and the principal part grows, until the last EMIs are almost all principal. Open the repayment schedule in any of our calculators to see this month by month.
How prepayment cuts the total
Because interest is charged on the balance, anything extra you pay early reduces every month's interest after it. On the same ₹50 lakh home loan at 8.5% for 20 years, paying ₹5,000 extra with every EMI clears the loan 4 years 5 months sooner and saves ₹13,89,250 in interest.
- Open the EMI calculator and enter your loan amount, rate and tenure.
- Turn on Prepay every month and set Extra each month, for example ₹5,000.
- Read how much sooner the loan ends and the interest saved, and open the schedule to see the new balance each year.
The calculator models a fixed extra amount every month; one-off lump-sum payments are not modelled. Under RBI rules, lenders generally may not charge prepayment or foreclosure fees on floating-rate loans taken by individuals. Fixed-rate loans, including many car and personal loans, often do carry a fee or a lock-in period, so read your loan agreement before you prepay.
Flat rate versus reducing rate
Be careful when a dealer, loan app or lender quotes a flat rate. A flat rate charges interest on the full loan amount for the whole tenure, even though you repay part of it every month. The same number as a reducing rate costs far less.
| ₹3,00,000 for 3 years | 12% reducing | 12% flat |
|---|---|---|
| EMI | ₹9,964 | ₹11,333 |
| Total interest | about ₹58,715 | ₹1,08,000 |
| Equivalent reducing rate | 12% | about 21.2% |
A 12% flat rate on this loan costs about the same as a 21% reducing rate. Always ask for the reducing-balance rate, or the annual percentage rate including fees, and compare offers on that. Our calculators use reducing-balance rates, so enter a flat rate only after converting it.
What the EMI does not include
- Processing fees and GST on them, insurance, stamp duty, registration, and legal or valuation charges. A processing fee taken from the amount paid out raises the real cost of the loan.
- Rate changes. Most home loans in India are floating and linked to an external benchmark such as the RBI repo rate. When the rate changes, the bank usually extends the tenure or changes the EMI. To recalculate, enter the outstanding balance from your loan statement, the new rate and the remaining tenure.
- Rounding. Your bank may round the EMI slightly differently, so expect small differences from the figures here.
Calculators assume the rate stays fixed for the whole tenure, so treat the result as a close estimate and check the final figures in your loan sanction letter.
Frequently asked questions
What is the formula to calculate EMI?
EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the loan amount, r is the annual rate divided by 12 and by 100, and n is the tenure in months. It assumes a monthly reducing balance, the method Indian banks use.
What is the EMI on a ₹50 lakh home loan for 20 years?
At 8.5% a year it is ₹43,391 a month. Over 20 years you pay ₹54,13,879 in interest, more than the loan itself. At a different rate the EMI changes, so enter the rate your lender quotes in the calculator.
Is it better to choose a shorter or longer tenure?
A longer tenure lowers the EMI but raises the total interest a lot. On ₹50 lakh at 8.5%, 25 years cuts the EMI by about ₹3,100 compared with 20 years, but the interest rises from about ₹54 lakh to about ₹71 lakh. Choose the shortest tenure whose EMI you can comfortably afford.
Does prepaying reduce my EMI or my tenure?
Either, depending on what you ask the bank for. Our calculator keeps the EMI the same and shows how much sooner the loan ends, which usually saves the most interest. Some banks let you lower the EMI instead after a prepayment.
How do I convert a flat interest rate to a reducing rate?
There is no simple multiplier, because it depends on the tenure, but for loans of one to seven years the equivalent reducing rate is roughly 1.6 to 1.8 times the flat rate. A 12% flat rate over 3 years equals about 21.2% reducing. Ask the lender for the reducing-balance rate to compare offers fairly.