How EMI is calculated: the loan formula, worked examples and the EMI Calculator
AdvertisementWhen you borrow money for a home, a car or a personal need, the bank does not ask you to repay the loan in one payment. It converts the loan into a fixed monthly payment called the EMI, short for equated monthly instalment. The number on the offer letter looks simple, but behind it is a formula that decides how much you really pay for the loan. The free EMI Calculator works out the monthly instalment, the total interest, the total repayment and a year-by-year schedule, in your browser. This guide explains the formula, walks through real numbers and shows how the choices you make change the cost.
What an EMI includes
Each EMI contains two parts:
- Interest: the cost of borrowing, charged on the balance you still owe.
- Principal: the part that reduces the amount you owe.
The EMI stays the same every month, but the mix changes. Interest is calculated on the outstanding balance, so in the first months the balance is high and most of the payment goes to interest. As the balance falls, the interest falls, and more of each payment goes to principal. This is called a reducing-balance loan, and it is what banks use for home, car and most personal loans.
The formula
The standard EMI formula is:
EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)
where:
- P is the loan amount (the principal),
- r is the monthly interest rate, which is the yearly rate divided by 12 and then by 100,
- n is the number of monthly instalments.
You do not have to compute it by hand, but it helps to see what each piece does. The part (1 + r)ⁿ is how much a rupee grows over the whole loan at the monthly rate. The formula picks the payment that exactly clears the debt, with interest, by the last month.
A worked example
A home loan of ₹10,00,000 at 8.5% a year for 20 years:
- P = 10,00,000
- r = 8.5 ÷ 12 ÷ 100 = 0.0070833
- n = 20 × 12 = 240
The EMI works out to about ₹8,678 a month. Over 240 months you pay 8,678 × 240, which is about ₹20,82,776. Subtract the ₹10,00,000 you borrowed and the interest cost is about ₹10,82,776. You repay more than twice what you received, which surprises many first-time borrowers.
Look at the first month. The interest for month one is 10,00,000 × 0.0070833 = ₹7,083. Of your ₹8,678 payment, only about ₹1,595 reduces the loan. That is why in the early years the balance falls slowly. Later the proportions reverse, and in the final years nearly the whole payment is principal.
How tenure changes the cost
The same loan with different tenures, at 8.5%:
| Tenure | EMI | Total interest | Total paid |
|---|---|---|---|
| 10 years | ₹12,399 | ₹4,87,828 | ₹14,87,828 |
| 15 years | ₹9,847 | ₹7,72,531 | ₹17,72,531 |
| 20 years | ₹8,678 | ₹10,82,776 | ₹20,82,776 |
A longer tenure lowers the monthly payment, which makes the loan easier to manage, but it increases the total interest by a large amount. Going from 15 to 20 years cuts the EMI by about ₹1,170 a month but adds over ₹3 lakh in interest. Do not choose a loan on the EMI alone; compare the total interest.
How the rate changes the cost
A small difference in the rate matters over a long loan. For ₹25,00,000 over 20 years:
| Rate | EMI | Total interest |
|---|---|---|
| 8.75% | ₹22,093 | ₹28,02,264 |
| 9.75% | ₹23,713 | ₹31,91,101 |
One percentage point more costs about ₹1,620 more every month and nearly ₹3.9 lakh over the loan. So negotiate the rate, and check whether your lender will lower it if your credit score improves. (These figures are standard calculations; your lender's figures can differ slightly.)
Using the calculator
- Open the EMI Calculator.
- Enter the loan amount and the yearly interest rate quoted by your lender.
- Enter the tenure and choose years or months.
- Read the monthly EMI, the total interest and the total payment. A bar shows the split between principal and interest.
- Scroll the year-by-year schedule to see, for every year, how much you paid, how much of it was interest and principal, and the balance left.
The tool accepts rates up to 50% and tenures from one month to 50 years, and shows a message if a value is out of range. The figures are calculated in your browser; nothing you enter is sent anywhere.
Reading the schedule
The schedule is the most useful part for planning. Look at how little the balance falls in year one compared with year ten. It explains two things:
- Prepaying early saves the most. A part-payment in year two removes principal that would have accrued interest for 18 more years. The same amount in year 18 saves very little.
- Selling or transferring early costs more than it seems. After five years of a 20-year loan, you have repaid a fifth of the principal, not a quarter of the total.
Ways to reduce the cost
- Make a larger down payment. Borrowing less cuts the interest in proportion.
- Choose the shortest tenure you can comfortably afford. Test two or three tenures in the calculator.
- Prepay when you can. Check your loan terms for prepayment charges; many floating-rate loans to individuals have none, but conditions vary.
- Increase the EMI each year as your income grows. Even a small step-up shortens the loan considerably.
- Compare the total cost, not just the rate. Processing fees, insurance bundled into the loan and legal charges all add up.
- Check the rate type. On a floating-rate loan, the lender may change the rate. It then either adjusts your EMI or your tenure, and you can re-run the calculator with the new rate and the remaining balance to see both.
What the calculator does not include
The result is the standard reducing-balance EMI. Your bank's actual schedule can differ a little because of:
- Processing fees, insurance or other charges added to the loan.
- The date of the first instalment, which may include a part-month of interest.
- Rounding rules each lender applies.
- Moratorium periods, as with education loans, when only interest is paid or nothing at all.
- Different calculation methods, such as a flat-rate loan, which charges interest on the full original amount for the whole term and so costs far more than the same stated rate on a reducing balance. Always ask which method applies.
Use the calculator to plan and compare. Use your lender's official schedule for the final numbers.
A quick affordability check
A common guideline is that all your EMIs together should stay under about 40% to 50% of your monthly take-home income, so that you keep room for living costs and for emergencies. If your income is ₹80,000 a month, EMIs of ₹32,000 to ₹40,000 in total are the upper limit of what most lenders and advisers consider comfortable. This is general guidance, not advice for your particular situation, so consider speaking to a qualified adviser before taking a large loan.
Related tools
Compare borrowing with saving using the SIP Calculator and the Compound Interest Calculator; both use the same idea of money growing month by month. For a deposit rather than a loan, use the FD & RD Calculator. To work out how much tax you may save on a home loan, start with the Income Tax Calculator. If you are writing the loan amount on a cheque or form, the Number to Words Converter spells it out. For the maths of the formula in a spreadsheet or in code, the PHP numbers and math lesson shows how to calculate and round money safely.
Quick answers
What does EMI stand for? Equated monthly instalment: the fixed amount you repay each month.
Why is the interest so high in the first years? Interest is charged on the outstanding balance, which is largest at the start.
Does a lower EMI mean a cheaper loan? Not necessarily. A longer tenure lowers the EMI and raises the total interest.
Is this the exact figure my bank will charge? It is the standard reducing-balance calculation. Fees and rounding can change it slightly.
Is my data stored? No. The calculation happens in your browser.