EMI Formula — How Banks Compute a Monthly Payment
An EMI — equated monthly instalment — is a fixed payment that clears a loan over a set number of months. The formula behind it is a geometric series in disguise, which makes it a good exercise for anyone who has met compound interest in school maths. It is also worth understanding for a much more practical reason: the same loan amount at the same interest rate can cost you twice as much, purely because of the tenure, and the formula shows exactly why.
All the rates below are illustrative. Interest rates vary between lenders, loan types and borrowers, so use whatever your lender has actually quoted in writing.
The formula
What each symbol means
- P — the principal, the amount actually borrowed. Not the price of the item; subtract the down payment first.
- i — the interest rate per month, as a decimal. If the annual rate is 9%, then i = 9 ÷ 12 ÷ 100 = 0.0075.
- n — the number of months in the tenure. Five years is n = 60.
Both conversions matter. Putting 9 or 0.09 in place of 0.0075, or 5 in place of 60, is the reason most hand calculations come out absurd.
Where the formula comes from
Each month, interest is charged on the balance that is still outstanding — this is called a reducing-balance loan. Write down the balance after each payment and you get a geometric series; setting the balance after month n to zero and solving for the payment gives the expression above. You do not need the derivation for the exam, but you do need one consequence of it: interest is charged on the shrinking balance, not on the original amount. That single fact is what separates a genuine EMI from a "flat rate" offer.
Worked example 1 — a ₹5,00,000 loan for 5 years at 9% p.a.
Step 1 — convert.
i = 9 ÷ 12 ÷ 100 = 0.0075
n = 5 × 12 = 60
Step 2 — the power term.
(1.0075)60 = 1.565681
Step 3 — substitute.
Numerator = 500 000 × 0.0075 × 1.565681 = 3750 × 1.565681 = 5871.30
Denominator = 1.565681 − 1 = 0.565681
EMI = 5871.30 ÷ 0.565681 = ₹10,379.18
Step 4 — the total cost.
Total paid = 10 379.18 × 60 = ₹6,22,750.70
Total interest = 6 22 750.70 − 5 00 000 = ₹1,22,750.70
Worked example 2 — the same loan over 10 years
Nothing changes except n. Watch what happens to the two numbers a borrower cares about.
i = 0.0075, n = 120, (1.0075)120 = 2.4513571
Numerator = 3750 × 2.4513571 = 9192.59
Denominator = 2.4513571 − 1 = 1.4513571
EMI = 9192.59 ÷ 1.4513571 = ₹6,333.79
Total paid = 6333.79 × 120 = ₹7,60,054.64
Total interest = ₹2,60,054.64
| Tenure | Monthly EMI | Total paid | Total interest |
|---|---|---|---|
| 5 years (60 months) | ₹10,379.18 | ₹6,22,750.70 | ₹1,22,750.70 |
| 10 years (120 months) | ₹6,333.79 | ₹7,60,054.64 | ₹2,60,054.64 |
Doubling the tenure cut the monthly payment by about 39%, but it more than doubled the interest — an extra ₹1,37,303.94. The EMI you can afford and the loan that costs least are two different questions, and the formula answers both.
Worked example 3 — how one instalment splits
Every EMI is part interest, part principal. The interest part is always calculated on the balance at the start of that month.
Take the 5-year loan of example 1, first month:
Interest portion = P × i = 500 000 × 0.0075 = ₹3,750.00
Principal portion = EMI − interest = 10 379.18 − 3750.00 = ₹6,629.18
New balance = 500 000 − 6629.18 = ₹4,93,370.82
Next month the interest portion is 493 370.82 × 0.0075 = ₹3,700.28, slightly less, so slightly more of the same EMI goes to principal. This shift accelerates every month, and by the final instalment almost the whole payment is principal.
This is why paying a lump sum early in the loan saves far more interest than the same sum paid near the end.
Worked example 4 — flat rate is not the same rate
Some lenders quote a "flat" rate, where interest is charged on the full original principal for the whole tenure, ignoring the fact that you are steadily repaying it.
Flat 9% on ₹5,00,000 for 5 years:
Interest = 500 000 × 0.09 × 5 = ₹2,25,000
Monthly payment = (500 000 + 225 000) ÷ 60 = ₹12,083.33
Compare with the reducing-balance EMI at the same quoted 9%: ₹10,379.18. The flat-rate version costs ₹1,704.15 more every month and ₹1,02,249.30 more in total, for the same headline percentage.
Whenever a rate is quoted, ask whether it is flat or reducing. A flat rate always sounds lower than the equivalent reducing-balance rate that would produce the same payments.
Tenure against total cost — the whole picture
Running the same ₹5,00,000 loan at 9% through four tenures shows the trade-off in a single table. Every row uses the formula exactly as in example 1; only n changes.
| Tenure | n | (1.0075)n | EMI | Total interest |
|---|---|---|---|---|
| 3 years | 36 | 1.308645 | ₹15,899.87 | ₹72,395.19 |
| 5 years | 60 | 1.565681 | ₹10,379.18 | ₹1,22,750.66 |
| 7 years | 84 | 1.873202 | ₹8,044.54 | ₹1,75,741.29 |
| 10 years | 120 | 2.451357 | ₹6,333.79 | ₹2,60,054.64 |
Read the two right-hand columns together. Going from 3 years to 10 years cuts the monthly payment by about 60%, and multiplies the interest by about 3.6. Neither column is "the answer" on its own: the EMI has to fit your monthly budget, and the interest column tells you what that comfort costs. The honest way to compare two loan offers is on total amount repaid, not on the EMI.
What the formula leaves out
The EMI is not the whole cost of a loan, and a calculator that shows only the EMI is showing you part of the picture. Before signing, add up:
- Processing fee, usually a percentage of the loan, charged up front, with GST on top of it.
- Insurance bundled with the loan, which is sometimes financed by increasing the principal — so it earns interest too.
- Prepayment or foreclosure charges, if any, which decide whether you can use a bonus to shorten the loan.
- Whether the rate is fixed or floating. A floating rate changes the EMI, or the tenure, or both, during the loan — so today's EMI is an estimate, not a promise.
Prepayment is where example 3 pays off. Because the early instalments are mostly interest, a lump sum paid in year one removes far more future interest than the same sum paid in the final year, when almost every rupee of the EMI is already going to principal.
Common mistakes
- Using the annual rate as i. Divide by 12 and by 100.
- Using years as n. The formula counts months, because the payment is monthly.
- Assuming a longer tenure is cheaper. It reduces the monthly outgo and increases the total cost.
- Comparing a flat rate with a reducing rate. They are not the same quantity and the same number means two very different loans.
- Forgetting everything outside the EMI — processing fees, insurance bundled with the loan and the GST charged on those fees are all real costs the formula does not contain.
- Rounding the power term too early. (1.0075)60 to two decimals shifts the EMI by several rupees a month, and by hundreds over the tenure.
Where this maths appears
| Context | Use |
|---|---|
| School maths (Class 8–10) | Compound interest and geometric progressions — the EMI formula is the same idea applied |
| Commerce and business studies | Annuities, present value, loan amortisation schedules |
| Aptitude and banking exams | Simple vs compound interest, instalment problems |
| Everyday life | Education loans, vehicle loans, comparing two offers honestly |
Try the numbers yourself. The Finance and Everyday section of the calculator suite includes an EMI calculator alongside GST, income tax and discount tools — change the tenure and watch the total interest move, exactly as in example 2.
Open the ABC Chemistry Calculator Suite →The suite is built mainly for Class 11–12 science students, and the same team teaches them: ABC Chemistry runs Class 11–12 chemistry coaching at its Gurugram centre plus online classes across India — abcchemistry.in.