=PMT() in a spreadsheet, or enter the three numbers in the free Loan EMI Calculator.What Is EMI (Equated Monthly Instalment)?
An EMI, or equated monthly instalment, is the fixed amount you pay your lender every month until a loan is fully repaid. The word “equated” is the key part: the payment stays the same each month, even though what it is made of changes. Every EMI contains some interest and some principal. Early in the loan most of the payment is interest; towards the end most of it is principal.
The term is used mainly by lenders in India, Pakistan, Bangladesh and other South Asian markets for home loans, personal loans, car loans and consumer finance. Lenders elsewhere usually call the same thing a “monthly payment”, and the maths behind it is identical.
The EMI Formula Explained
Nearly every reducing-balance loan uses the same formula:
EMI = P × r × (1 + r)n / ((1 + r)n − 1)
What P, r and n mean
- P (principal): the amount you borrow, before any interest.
- r (monthly interest rate): the annual rate converted to a monthly decimal.
- n (number of instalments): the tenure in months, not years. A 20-year home loan is n = 240.
The (1 + r)n term appears twice. In the numerator it shows how much the balance would grow if interest compounded for the whole term. In the denominator, subtracting 1 isolates the growth part, which is then spread evenly across every instalment. That is why the payment comes out the same every month.
Converting an annual rate to a monthly rate
Lenders quote annual rates, but the formula needs a monthly decimal. Divide the annual rate by 12, then by 100:
- 8.5% a year → 8.5 ÷ 12 ÷ 100 = 0.0070833
- 12% a year → 12 ÷ 12 ÷ 100 = 0.01
- 9% a year → 9 ÷ 12 ÷ 100 = 0.0075
Keep at least six decimal places. Rounding r too early is one of the most common reasons a hand calculation ends up a few rupees or dollars off.
How to Calculate EMI Manually (Step by Step)
Here is the full calculation for a ₹20,00,000 home loan at 8.5% a year over 20 years, with no steps skipped.
- Find r. 8.5 ÷ 12 ÷ 100 = 0.00708333
- Find n. 20 years × 12 = 240 months
- Find (1 + r)n. (1.00708333)240 ≈ 5.4412
- Calculate the top half. 20,00,000 × 0.00708333 × 5.4412 ≈ 77,084
- Calculate the bottom half. 5.4412 − 1 = 4.4412
- Divide. 77,084 ÷ 4.4412 ≈ ₹17,356 (₹17,356.46 at full precision)
Personal loan EMI by hand
The same steps work for a personal loan, and the numbers are easier because the monthly rate is a round figure. For ₹5,00,000 at 12% a year over 5 years:
- Find r. 12 ÷ 12 ÷ 100 = 0.01
- Find n. 5 years × 12 = 60 months
- Find (1 + r)n. (1.01)60 ≈ 1.8167
- Top half. 5,00,000 × 0.01 × 1.8167 ≈ 9,083.5
- Bottom half. 1.8167 − 1 = 0.8167
- Divide. 9,083.5 ÷ 0.8167 ≈ ₹11,122 (₹11,122.22 at full precision)
On a basic phone calculator, work out (1.01)60 by multiplying 1.01 by itself 60 times or using the xy key, write the result down, then do the top half, the bottom half and the division in that order.
If you’d rather not raise a number to the 240th power by hand, the Loan EMI Calculator runs the same formula and shows the full repayment breakdown.
EMI Calculation Examples
The examples below use the reducing-balance formula above. The interest rates are illustrative only, chosen to show how the maths works. They are not current lender rates. Your actual rate depends on the lender, your credit profile and the loan type.
| Loan type | Amount | Rate (illustrative) | Tenure | EMI | Total interest | Total paid |
|---|---|---|---|---|---|---|
| Home loan | ₹20,00,000 | 8.5% | 20 years | ₹17,356.46 | ₹21,65,551.52 | ₹41,65,551.52 |
| Personal loan | ₹5,00,000 | 12% | 5 years | ₹11,122.22 | ₹1,67,333.43 | ₹6,67,333.43 |
| Car loan | ₹8,00,000 | 9% | 7 years | ₹12,871.26 | ₹2,81,186.06 | ₹10,81,186.06 |
| Small loan | $10,000 | 10% | 1 year | $879.16 | $549.91 | $10,549.91 |
Home loan EMI example
A ₹20,00,000 home loan at 8.5% over 20 years (240 months) costs ₹17,356.46 a month. Over the full term you repay ₹41,65,551.52, which means the interest (₹21,65,551.52) is larger than the amount borrowed. That is normal for long tenures: the balance stays high for many years, so interest keeps accruing on a large base.
Personal loan EMI example
A ₹5,00,000 personal loan at 12% over 5 years (60 months) works out to ₹11,122.22 a month. Here r = 0.01 exactly, which makes it a good example to check by hand. Total interest is ₹1,67,333.43, about a third of the principal, because the tenure is much shorter than a home loan’s.
Car loan EMI example
A ₹8,00,000 car loan at 9% over 7 years (84 months) gives an EMI of ₹12,871.26 and total interest of ₹2,81,186.06. Car loans sit between personal and home loans in both tenure and total interest.
Small loan example: $10,000 at 10% over 12 months
The formula works the same way in any currency. For $10,000 at 10% over 12 months:
- r = 10 ÷ 12 ÷ 100 = 0.008333
- (1.008333)12 = 1.104713
- EMI = 10,000 × 0.008333 × 1.104713 / (1.104713 − 1) = 92.06 / 0.104713 = $879.16
Across 12 payments you pay about $549.91 in interest on top of the $10,000 principal.
How Each EMI Splits Into Interest and Principal (Amortization Table)
The EMI stays fixed, but the split changes every month. Each month’s interest is the outstanding balance × r. Whatever is left of the EMI goes towards the principal, so the balance falls a little faster each month. Here are the first three months of the ₹20,00,000 home loan example:
| Month | EMI | Interest | Principal | Closing balance |
|---|---|---|---|---|
| 1 | ₹17,356.46 | ₹14,166.67 | ₹3,189.79 | ₹19,96,810.21 |
| 2 | ₹17,356.46 | ₹14,144.07 | ₹3,212.39 | ₹19,93,597.82 |
| 3 | ₹17,356.46 | ₹14,121.32 | ₹3,235.14 | ₹19,90,362.68 |
In month 1, more than 80% of the payment is interest. That share shrinks every month as the balance drops. It is also why a prepayment early in a long loan saves far more interest than the same prepayment near the end. Real lender schedules may adjust the final instalment by a few paise or cents for rounding, and that is normal.
Reducing Balance vs Flat Rate EMI
Two loans quoted at the “same” rate can cost very different amounts, depending on how interest is calculated.
- Reducing balance (also called diminishing balance) charges interest each month only on the principal still outstanding. This is the method behind the EMI formula above.
- Flat rate charges interest on the full original principal for the entire term, adds it to the principal, and divides the total evenly across all instalments.
Using the ₹5,00,000 personal loan at 12% over 5 years:
| Method | Monthly EMI | Total interest |
|---|---|---|
| Reducing balance | ₹11,122.22 | ₹1,67,333.43 |
| Flat rate (5,00,000 × 12% × 5 = 3,00,000 interest; 8,00,000 ÷ 60) | ₹13,333.33 | ₹3,00,000.00 |
Same principal, same quoted rate, same tenure, yet the flat-rate loan costs ₹2,211.11 more every month. Before comparing offers, ask each lender which method it uses. If you’re quoted a flat rate, the reducing-balance formula will not give you the right EMI.
How to Calculate EMI in Excel or Google Sheets
Both Excel and Google Sheets have a built-in PMT function that returns the same result as the formula:
=PMT(8.5%/12, 240, -2000000)
This returns 17,356.46 for the home loan example. The three arguments are the monthly rate, the number of months, and the principal. The principal is entered as a negative number because of the function’s cash-flow sign convention; leave the minus sign off and you get a negative EMI. A spreadsheet is also the easiest way to build a full month-by-month schedule: interest = previous balance × monthly rate, principal = EMI − interest, new balance = previous balance − principal.
Working backwards: how much can you borrow for a given EMI?
If you know the EMI you can afford, rearrange the formula to find the loan amount: P = EMI × ((1 + r)n − 1) / (r × (1 + r)n). For an EMI of ₹15,000 at an illustrative 9% over 15 years (r = 0.0075, n = 180), that comes to about ₹14,78,901. In a spreadsheet, =PV(9%/12, 180, -15000) returns the same figure.
How Tenure and Interest Rate Change Your EMI
A longer tenure lowers the EMI but raises the total interest. A higher rate raises both. Here is the same ₹20,00,000 principal under different illustrative scenarios:
| Rate (illustrative) | Tenure | EMI | Total interest | Total paid |
|---|---|---|---|---|
| 8.5% | 15 years | ₹19,694.79 | ₹15,45,062.41 | ₹35,45,062.41 |
| 8.5% | 20 years | ₹17,356.46 | ₹21,65,551.52 | ₹41,65,551.52 |
| 8.5% | 25 years | ₹16,104.54 | ₹28,31,362.50 | ₹48,31,362.50 |
| 7.5% | 20 years | ₹16,111.86 | ₹18,66,847.33 | ₹38,66,847.33 |
| 9.5% | 20 years | ₹18,642.62 | ₹24,74,229.70 | ₹44,74,229.70 |
Going from 20 to 25 years cuts the EMI by about ₹1,252 a month but adds roughly ₹6.66 lakh in interest. A one-point change in the rate moves the EMI by roughly ₹1,245 to ₹1,286 a month on this loan. To compare scenarios for a property purchase in more detail, the Mortgage Calculator is built for long tenures.
What Is Pre-EMI?
Some home loans for under-construction property are disbursed in stages. Until the full amount is released and regular EMIs begin, many lenders charge a pre-EMI: interest only, on the amount disbursed so far. It’s calculated as disbursed amount × annual rate ÷ 12. If ₹10,00,000 has been disbursed at an illustrative 8.5%, the pre-EMI is 10,00,000 × 0.085 ÷ 12 ≈ ₹7,083.33 a month.
Pre-EMI payments don’t reduce the principal, so a long construction period adds interest cost without shortening the loan. Whether pre-EMI applies, and when full EMIs start, depends on your lender’s terms, so check the sanction letter.
Calculate Your EMI Instantly
Enter your loan amount, rate and tenure in the free Loan EMI Calculator to see your EMI and full repayment breakdown. It runs in your browser, so your loan details are not sent to a server.
Keep in mind that a lender’s final EMI can differ from any calculator’s figure. Processing fees, insurance premiums bundled into the loan, and the lender’s own rounding or compounding conventions all affect the number, and rates vary by lender and borrower. Use the calculator to plan and compare, then confirm the exact figure in your loan agreement.
For related maths, the Simple Interest Calculator shows how flat-style interest adds up, the Compound Interest Calculator shows the same compounding applied to savings, and the Percentage Calculator helps when you want to see interest as a share of the total. If you run a business and need other money calculators, see our roundup of free small business calculators.
Frequently Asked Questions
What is EMI in a loan?
EMI stands for equated monthly instalment. It is the fixed amount you pay your lender every month until the loan is repaid. Each EMI covers that month’s interest plus part of the principal, and the share going to principal grows as the balance falls.
Is EMI calculated on a reducing balance?
Most home, car and personal loans from banks use the reducing-balance method, where interest is charged only on the outstanding principal. Some lenders, particularly for consumer and vehicle finance, quote a flat rate instead, which costs more for the same headline rate. Your loan agreement states which method applies.
How do I calculate EMI for a home loan?
Convert the annual rate to a monthly decimal (rate ÷ 12 ÷ 100), convert the tenure to months, and apply EMI = P × r × (1 + r)n / ((1 + r)n − 1). For ₹20,00,000 at an illustrative 8.5% over 20 years, that gives ₹17,356.46 a month.
Does a longer tenure mean more total interest?
Yes. A longer tenure lowers the EMI, but the balance stays higher for longer, so more interest accrues. On ₹20,00,000 at 8.5%, moving from 20 to 25 years lowers the EMI by about ₹1,252 but adds roughly ₹6.66 lakh in total interest.
Does a prepayment reduce my EMI or my tenure?
It depends on the lender and the loan agreement. Some lenders keep the EMI fixed and shorten the tenure; others keep the tenure and reduce the EMI. Either way, a prepayment lowers the principal, which reduces the total interest you pay over the remaining term.
Why does my lender’s EMI not match my own calculation?
Common reasons are a processing fee or insurance premium added to the loan amount, a flat-rate calculation instead of reducing balance, different compounding conventions, or rounding. Check that you entered n in months and used the rate stated in your loan agreement rather than an advertised headline rate.
The Bottom Line
EMI is three inputs and one formula: principal, monthly rate and number of months. Convert the rate and tenure into monthly units, apply the formula or =PMT(), and you get the same reducing-balance figure a lender uses before fees. Treat the rates in this guide as illustrative, confirm the method and charges with your lender, and use the Loan EMI Calculator to compare tenures and rates quickly.
