An EMI, or equated monthly instalment, is the fixed amount you pay every month on a loan until it is cleared. Banks and calculators produce it instantly, which is convenient and also hides how much of each payment is interest. This guide works through one loan by hand, shows how to reproduce every number in Excel, and then uses the same arithmetic to answer the questions that actually change what you pay: how long to borrow for, and what a prepayment does.
The formula
EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
- P is the amount borrowed.
- r is the monthly interest rate as a decimal: the annual rate divided by 12, then by 100. A 9% annual rate is 0.09 ÷ 12 = 0.0075.
- n is the number of monthly payments: 5 years is 60.
The formula comes from one requirement: a fixed payment, made every month, must pay that month's interest on whatever is still owed and clear the balance exactly at the last payment. It applies to reducing-balance loans, where interest is charged only on what you still owe, which is how home loans and most car and personal loans from banks work.
A worked example
Borrow ₹10,00,000 at 9% a year for 5 years.
P = 10,00,000
r = 9 ÷ 12 ÷ 100 = 0.0075
n = 5 × 12 = 60
(1 + r)^n = 1.0075^60 = 1.565681
EMI = 10,00,000 × 0.0075 × 1.565681 ÷ (1.565681 − 1)
= 11,742.61 ÷ 0.565681
= ₹20,758.36Over 60 months you pay 60 × 20,758.36, about ₹12,45,501. The difference from what you borrowed, about ₹2,45,501, is the interest.
Checking it in Excel
Excel has the formula built in:
=PMT(9%/12, 60, -1000000) → 20,758.36 =IPMT(9%/12, 1, 60, -1000000) → 7,500.00 interest in month 1 =PPMT(9%/12, 1, 60, -1000000) → 13,258.36 principal in month 1 =-CUMIPMT(9%/12, 60, 1000000, 1, 60, 0) → 2,45,501.31 total interest
The minus sign in front of the loan amount is Excel's convention: money you receive and money you pay have opposite signs. Leave it out and PMT gives the same number, negative.
To see every month, build a schedule. Put the rate in B1 (9%), the EMI in B2 (=PMT(B1/12,60,-1000000)), and start the table in row 5:
A B C D E 4 Month Opening balance Interest Principal Closing balance 5 1 1000000 =B5*$B$1/12 =$B$2-C5 =B5-D5 6 2 =E5 =B6*$B$1/12 =$B$2-C6 =B6-D6
Fill row 6 down to month 60. The closing balance in the last row should be zero, give or take a fraction of a rupee from rounding. If it is, your schedule is right. The site's amortization schedule produces the same table.
How each EMI splits into interest and principal
Every month, interest is charged on the balance still owed, and whatever is left of the EMI repays principal:
Month 1: interest = 10,00,000 × 0.0075 = 7,500.00
principal = 20,758.36 − 7,500.00 = 13,258.36
balance = 10,00,000 − 13,258.36 = 9,86,741.64
Month 2: interest = 9,86,741.64 × 0.0075 = 7,400.56
principal = 20,758.36 − 7,400.56 = 13,357.79
balance = 9,73,383.85The EMI stays the same; the split moves. In month 60 only about ₹155 of the payment is interest. Because interest is front-loaded, the first year of this loan carries about a third of all the interest you will ever pay on it: ₹83,270 of the ₹2,45,501.
On a long home loan the effect is far stronger. ₹50,00,000 at 8.5% over 20 years has an EMI of ₹43,391. In the first month, ₹35,417 of that is interest and only ₹7,974 repays the loan. The principal part does not overtake the interest until month 143, nearly twelve years in.
What tenure does
The same ₹10,00,000 at 9%, over different terms:
| Tenure | EMI | Total interest |
|---|---|---|
| 3 years | ₹31,799.73 | ₹1,44,790 |
| 5 years | ₹20,758.36 | ₹2,45,501 |
| 7 years | ₹16,089.08 | ₹3,51,483 |
| 10 years | ₹12,667.58 | ₹5,20,109 |
Doubling the term from 5 to 10 years cuts the EMI by under 40% and more than doubles the interest. A longer tenure buys a lower monthly payment, and you pay for it in total cost. Choose the shortest tenure whose EMI you can carry comfortably even in a bad month, not the one with the smallest EMI on offer. The loan comparison calculator shows two offers side by side.
What a prepayment does
Suppose that after the 12th EMI you pay an extra ₹1,00,000. At that point you owe ₹8,34,169.98, so the balance drops to ₹7,34,169.98. With 48 months left, the lender will usually let you choose between two things:
| Choice | What happens | Interest from here on | Saved |
|---|---|---|---|
| No prepayment | 48 more EMIs of ₹20,758.36 | ₹1,62,231 | |
| Keep the EMI, shorten the loan | 41 EMIs of ₹20,758.36 and a last payment of about ₹5,238 | ₹1,22,161 | ₹40,070 |
| Keep the tenure, lower the EMI | 48 EMIs of ₹18,269.85 | ₹1,42,783 | ₹19,448 |
The same ₹1,00,000 saves about twice as much interest when you keep paying the same EMI. That is the general rule: shortening the tenure saves more, because the larger payments keep cutting into the balance. Lowering the EMI is the right choice when you need the monthly room.
In Excel, the shorter term after the prepayment is:
=NPER(9%/12, -20758.36, 734169.98) → 41.25 months
and the lower EMI is:
=PMT(9%/12, 48, -734169.98) → 18,269.85
A prepayment saves the most early in the loan, when the balance is largest. In India, lenders are not permitted to charge individuals a penalty for prepaying a floating-rate loan taken for non-business purposes; fixed-rate loans may carry a charge. Read your own loan agreement before deciding.
Watch for flat-rate quotes
Some lenders, especially for vehicles and consumer goods, quote a flat rate: interest worked out on the full original amount for the whole term, however much you have repaid. A 9% flat rate on ₹10,00,000 over 5 years means ₹4,50,000 of interest and an EMI of ₹24,166.67. The same EMI on a reducing-balance loan corresponds to a rate of about 15.7%. When a quote does not say "reducing balance", ask.
Why the bank's figure may differ slightly
- Some lenders calculate interest daily rather than monthly, which moves the figures by small amounts.
- The first instalment can include extra interest for the days between disbursement and the start of the EMI cycle.
- Processing fees, insurance and taxes are not part of the EMI formula, but they are part of what you pay.
- On a floating-rate loan the rate changes over time, and the lender then changes the EMI, the tenure, or both.
The EMI calculator uses exactly the formula above, with the full amortization schedule and a borrowing-power check. As with any calculator, its results are estimates, not financial advice: your lender's sanction letter and schedule are the figures that count.