How EMI Is Calculated: Formula, Worked Example and Amortisation

Most people know their EMI to the rupee. It's the amount that leaves the account a few days after salary credit, every month, for years. Far fewer people know how the bank arrived at that number, or why, after three years of paying a home loan EMI, the outstanding balance has barely moved.

The maths behind an EMI is not hard. Once you see it, a lot of loan decisions get easier: how long a tenure to pick, whether to prepay, what to do when the bank says your rate has gone up. And by the end you should be able to pick up your own loan statement and check the bank's figures yourself.

One fixed payment, two moving parts

EMI stands for equated monthly instalment. "Equated" is the key word. You pay the same amount every month, but what that amount does changes every single month.

Each EMI has two parts. One part is the interest for that month, charged on whatever you still owe. The rest goes towards the loan itself (the principal) and brings the balance down. Next month the balance is a little smaller, so the interest part is a little smaller, and since the EMI is fixed, a little more goes to principal. This repeats till the balance hits zero on the last EMI.

This is called the reducing balance method, and it's how almost all home loans, car loans from banks and personal loans are worked out in India. You only pay interest on money you still owe, not on what you've already returned.

The formula every bank uses

Bank software, loan apps and the EMI calculators online all run this one formula:

EMI = P × r × (1 + r)n ÷ ((1 + r)n − 1)

• P is the loan amount, the principal.
• r is the monthly interest rate: the yearly rate divided by 12, then by 100. So 9% a year becomes 0.0075.
• n is the number of monthly EMIs. A 5-year loan has 60, a 20-year loan has 240.

No need to memorise it. It finds the one fixed monthly amount that clears P in exactly n months when interest is charged every month on the remaining balance. The (1 + r)ⁿ part is compounding, how much ₹1 grows to at that rate over the full tenure.

One thing people trip on: the rate you're quoted (say 8.5%) is a yearly rate, but interest is charged monthly. Use the yearly rate as is in the formula and you'll get a nonsense answer.

Working it out by hand: ₹10 lakh at 9% for 5 years

Take a ₹10 lakh loan at 9% a year for 5 years, say a car loan. Keep a phone calculator handy.

1. Monthly rate: 9 ÷ 12 ÷ 100 = 0.0075.
2. Number of EMIs: 5 × 12 = 60.
3. (1 + r)ⁿ: 1.0075 to the power 60 = 1.56568. (Any scientific calculator does this. On a basic phone calculator, turn it sideways.)
4. Top part: 10,00,000 × 0.0075 × 1.56568 = 11,742.61.
5. Bottom part: 1.56568 − 1 = 0.56568.
6. EMI: 11,742.61 ÷ 0.56568 = ₹20,758.

The EMI calculator shows ₹20,758.36, so the hand method matches. In Excel or Google Sheets, =PMT(9%/12, 60, -1000000) gives the same figure.

Now the useful part. 60 EMIs of ₹20,758 add up to ₹12,45,501. You borrowed ₹10 lakh, so the loan cost you ₹2,45,501 in interest, about a quarter of the amount borrowed.

Month by month: where each EMI goes

Here is the same ₹10 lakh loan, month by month. This is called an amortisation schedule, and your lender has to give you one.

Month 1 interest is easy to check: ₹10,00,000 × 0.0075 = ₹7,500. Whatever is left of the EMI, ₹13,258, cuts the balance. Month 2 interest is charged on ₹9,86,742, so it's a bit lower. By the last month, interest is just ₹155.

Year-wise, the calculator shows you pay ₹83,270 as interest in year 1 and only ₹11,730 in year 5, even though the EMIs paid in both years are the same ₹2,49,100.

Why a home loan feels like "only interest" for years

On a 5-year loan the shift from interest to principal happens fast. On a 20-year home loan it's painfully slow, and this is where most people get a shock.

Take a ₹30 lakh home loan at 8.5% for 20 years. The EMI is ₹26,035. In the very first month, interest is ₹21,250 and only ₹4,785 goes towards the loan.

In year 1, about 81% of what you pay is interest. After ten years and ₹31 lakh of EMIs, you still owe about ₹21 lakh. The principal part overtakes the interest part only around year 12, and the balance falls to half (₹15 lakh) only in year 14. Over the full 20 years you pay ₹32.5 lakh as interest, more than the loan itself.

Nobody is cheating you here. The interest is just 8.5% on a big balance, and the balance stays big because the EMI is spread thin over 240 months. But it does tell you when extra money hurts the loan most: early. Prepay ₹1 lakh right after the 12th EMI and keep the EMI the same, and the loan finishes about 18 EMIs sooner, saving roughly ₹3.7 lakh of interest. The same ₹1 lakh in year 17 saves far less. For floating-rate loans taken by individuals for personal use, banks can't charge a prepayment penalty. More on this in reduce EMI or reduce tenure after prepaying.

When the dealer quotes a "flat" rate

Everything above is reducing balance. Some lenders, especially for consumer durables, two-wheelers and some car dealer finance, quote a flat rate instead. It sounds cheaper and it isn't.

With a flat rate, interest is charged on the full original amount for the whole tenure, even though you are paying it back every month. Say a ₹3 lakh loan at "flat 10%" for 3 years:

• Interest = ₹3,00,000 × 10% × 3 = ₹90,000.
• EMI = (₹3,00,000 + ₹90,000) ÷ 36 = ₹10,833.

A genuine 10% reducing-balance loan of ₹3 lakh for 3 years has an EMI of ₹9,680 and total interest of ₹48,486. To get an EMI of ₹10,833 on reducing balance, the rate has to be about 17.9%. So "flat 10%" is really close to 18%. We go through the conversion in detail in flat rate vs reducing balance rate.

The good news is that RBI now requires a Key Facts Statement (KFS) for every new retail loan sanctioned from 1 October 2024. It must show the annual percentage rate (APR), which includes the fees, and the full repayment schedule. If a dealer quotes a flat rate, ask for the KFS and look at the APR.

What moves your EMI: amount, rate and tenure

Only three things go into the formula, so only three things change the EMI.

Loan amount

Double the loan, double the EMI. At 8.5% for 20 years, every ₹1 lakh borrowed costs about ₹868 a month. So ₹30 lakh is ₹26,035 and ₹40 lakh would be about ₹34,713. A bigger down payment is the simplest way to a smaller EMI.

Tenure

Here's the same ₹30 lakh at 8.5% over different tenures:

Look at the pattern. Going from 10 to 15 years cuts the EMI by over ₹7,600. Going from 25 to 30 years cuts it by only about ₹1,100, but adds more than ₹10 lakh of interest. Beyond 20 years, each extra year buys you very little relief. A longer tenure has one real upside: the lower EMI makes it easier to qualify and leaves room in a tight budget. The downside is the interest bill, and that's the part a sales pitch leaves out. A dealer or DSA who says "only ₹23,000 a month" on a 30-year tenure is selling you ₹53 lakh of interest on a ₹30 lakh loan, so always ask for the total interest along with the EMI. The 20 vs 30 year home loan post goes deeper on choosing.

Interest rate

Same ₹30 lakh, 20 years, different rates:

Each 0.5% is roughly ₹950 a month on this loan, and ₹2.2–2.3 lakh of extra interest over 20 years. That's why a good credit score, which gets you a lower rate, is worth more than people think. Big banks are quoting home loans from about 7.25% up to around 9% depending on your profile, and personal loans usually start near 10% and go well above 15%. These cards change often, so check the lender's current rate before you compare.

When the rate changes in the middle of the loan

Most new home loans today are floating-rate and linked to RBI's repo rate. On 7 October 2026, RBI raised the repo rate by 0.25% to 5.50%, and several banks raised their repo-linked lending rates the same week. So for lakhs of borrowers, the "r" in the formula just changed.

When that happens, the bank recalculates using your remaining balance and remaining months. It can either raise the EMI or keep the EMI the same and stretch the tenure. Many banks stretch the tenure by default, and a lot of borrowers never notice. A 20-year loan can turn into 21 or 22 years this way without the EMI moving by a rupee. Under RBI's rules on EMI resets, the bank has to tell you, and you get to choose: higher EMI, longer tenure, a mix of both, or prepay. You also get a quarterly statement showing principal and interest paid so far and EMIs left.

Back to the ₹30 lakh loan at 8.5%. After 3 years, the balance is about ₹28.05 lakh with 204 EMIs left. Now the rate goes up:

If the extra ₹426 or ₹856 a month fits your budget, raising the EMI costs less than half as much as the quiet tenure extension. Ask your bank in writing which option they have applied. The repo rate and your home loan EMI post has more on this.

What the EMI number leaves out

The EMI formula only covers principal and interest. The real cost of a loan has a few more pieces:

• Processing fee: charged upfront, plus GST. On personal loans it can be a couple of percent of the loan, cut from the amount you get.
• Broken-period interest: if the loan is disbursed on the 18th and your EMI date is the 5th, the lender charges interest for the gap days separately. It's usually small.
• Pre-EMI on under-construction flats: the bank releases the loan to the builder in stages as construction moves ahead, and till then you pay interest only on what has been released. Full EMIs start later. Pre-EMI doesn't reduce your loan at all.
• Insurance: loan protection cover is often bundled in, sometimes added to the loan amount itself, which means you pay interest on the premium too. Ask whether it's optional.

All of these have to appear in the KFS, and charges not mentioned there can't be added later without your consent.

One more limit is worth setting for yourself. Banks may allow all your EMIs together to take 50% or more of take-home pay. That's their comfort, not yours. Keeping total EMIs within about 30–40% leaves room for school fees, medical bills and a job change. Before you sign, check how much you can actually borrow against your salary on the home loan eligibility calculator, and work out the EMI on the home loan EMI calculator, car loan EMI calculator or personal loan EMI calculator as the case may be.

Check your own loan in ten minutes

None of this has to stay theory. You can check what the bank is doing on your own loan with two documents and a spreadsheet. Keep the sanction letter or KFS handy (original amount, rate, tenure) and your latest loan statement or repayment schedule, which most banks let you download from net banking. Then go through these in order.

1. Check the EMI. In Excel or Google Sheets, type =PMT(yearly rate/12, months, -loan amount) with the figures from your sanction letter. For the ₹30 lakh loan above, =PMT(8.5%/12, 240, -3000000) gives ₹26,034.70, which the bank rounds to ₹26,035. If your actual EMI is a few hundred rupees off, either the rate has changed since the loan started or something like an insurance premium was added to the loan amount. Find out which before going further.
2. Check one month's interest. Take the balance at the start of any month, multiply by the yearly rate and divide by 12. On the same loan, the balance after the first year is ₹29,40,293, so month 13's interest should be ₹29,40,293 × 8.5% ÷ 12 = ₹20,827, and the other ₹5,208 of the EMI should show up as principal. Banks that charge by the actual number of days will be slightly off in 31-day months and in February. A gap of a few thousand is something else, and worth a question.
3. Check the outstanding. =FV(yearly rate/12, EMIs paid, EMI, -loan amount) gives the balance after any number of EMIs. =FV(8.5%/12, 12, 26035, -3000000) returns ₹29,40,289, a few rupees away from the schedule only because the EMI is rounded. If your statement shows clearly more owed than this, look for pre-EMI months, a bounced EMI, or a rate change you missed. If the rate has changed, redo the check from the last reset date: balance on that day, new rate, months left.
4. Check how many EMIs are left. =NPER(yearly rate/12, -EMI, outstanding) tells you the months left at today's rate. Take the ₹28.05 lakh balance from the rate-reset example: =NPER(8.75%/12, -26035, 2805000) comes to about 212 months, not the 204 that were left before the rise. If the EMIs left on your statement are more than the original tenure minus the EMIs you've paid, your loan has been stretched.
5. Work out the interest still to come. EMI × EMIs left, minus the outstanding. With 204 EMIs of ₹26,035 left on ₹28.05 lakh, that is about ₹25 lakh. This is the number any prepayment eats into, which is why the same ₹1 lakh does so much more early in the loan than near the end.

Most of the time the numbers will match, and that is useful in itself, because you now know exactly what the loan costs you and where an extra rupee helps it most. If they don't match, don't argue on the phone. Write to the bank and ask for the rate applied on each date since disbursal, a fresh repayment schedule at today's rate, and whether any rate rise was handled by extending the tenure. The RBI reset rules linked above already make them tell you about any change to your EMI or tenure, so a written request usually gets a straight answer. Do it once a year, and again whenever a letter about your rate arrives.

Written by the Gainly team for general information, not as investment or tax advice. Rates and rules change, so check the latest before you decide; tell us if something here is out of date. Contact