An Equated Monthly Instalment (EMI) is a fixed payment made every month until a loan is fully repaid. The amount stays the same, but its composition changes: early instalments are mostly interest, later ones are mostly principal.
This guide derives the EMI formula, works through it by hand, builds a short amortisation schedule so you can see exactly where the money goes, and shows how to verify a lender's figure.
Every number below can be reproduced with the EMI Calculator.
The EMI Formula
Where:
- P — principal, the amount actually borrowed after any down payment or processing deduction
- r — interest rate per month expressed as a decimal, i.e. annual rate ÷ 12 ÷ 100
- n — total number of monthly instalments (years × 12)
- ^ — exponentiation
The formula assumes a fixed interest rate, monthly compounding, equal payments and no missed instalments.
Converting the rate correctly
An annual rate of 9.5 percent becomes:
Using 0.095 or 9.5 directly is the most common source of a wrong answer.
Worked Example 1: Home Loan
Principal ₹40,00,000, annual rate 8.5 percent, tenure 20 years.
EMI ≈ ₹34,713 per month.
Step 5 — total cost
Over twenty years, the interest exceeds the original principal.
Worked Example 2: Car Loan
Total paid = 17,110 × 60 = ₹10,26,600, of which ₹2,26,600 is interest.
Notice how much lower the interest share is than the home loan, despite a higher rate — tenure drives total interest more than the rate does.
Worked Example 3: Personal Loan
How an Amortisation Schedule Works
Each month:
Principal repaid = EMI − Interest
New balance = Outstanding balance − Principal repaid
Using the car loan above (₹8,00,000 at 10.25 percent, EMI ₹17,110):
| Month | Opening balance | Interest | Principal | Closing balance |
|---|---|---|---|---|
| 1 | 8,00,000 | 6,833 | 10,277 | 7,89,723 |
| 2 | 7,89,723 | 6,746 | 10,364 | 7,79,359 |
| 3 | 7,79,359 | 6,657 | 10,453 | 7,68,906 |
| 4 | 7,68,906 | 6,568 | 10,542 | 7,58,364 |
| 5 | 7,58,364 | 6,478 | 10,632 | 7,47,732 |
The instalment never changes, but the interest component falls every month and the principal component rises by exactly the same amount. By the final instalment, almost all of the payment is principal.
This front-loading is why repaying early saves so much — and why the first years of a long loan reduce the balance so slowly.
Checking a Lender's EMI Quote
Three things commonly explain a mismatch between your calculation and the quoted figure:
1. Processing fee treatment. If a fee is deducted from disbursal, you receive less than P but repay on the full P.
2. Rounding. Lenders usually round the EMI up to the nearest rupee and adjust the final instalment.
3. Interest calculation basis. Reducing-balance monthly is standard; a flat-rate quote produces a very different effective cost.
Flat rate versus reducing balance
The same EMI under a reducing-balance calculation corresponds to an annual rate of roughly 12.9 percent. A flat rate always understates the true cost because it charges interest on the original principal even after most of it has been repaid.
Assumptions and Limitations
- The rate is fixed for the whole tenure. Floating-rate loans reset periodically, changing either the EMI or the tenure.
- No prepayments, part-payments or missed instalments.
- Insurance premiums, processing fees and statutory charges are excluded.
- The first instalment starts one full month after disbursal; a longer gap adds broken-period interest.
An EMI figure is an arithmetic result under these assumptions, not a personalised affordability assessment or financial advice.
Common Mistakes
- Using the annual rate instead of the monthly rate.
- Using the years instead of the number of months for n.
- Subtracting 1 from the wrong term — the denominator is (1 + r)^n − 1, not (1 + r)^(n − 1).
- Forgetting that a longer tenure lowers the EMI while raising total interest.
- Comparing a flat rate with a reducing-balance rate as if they were the same.
Interpreting the Result
Look at three numbers together, not just the instalment:
- EMI — what your monthly budget must absorb
- Total interest — the real cost of borrowing
- Interest as a share of principal — an easy way to compare offers of different tenures
Lenders commonly look for total EMIs to stay within roughly 40 to 50 percent of net monthly income, though the exact policy varies by lender and product.
Related Calculations
- EMI Calculator — instant EMI with amortisation breakdown
- Loan Calculator — total interest and repayment schedule
- Compound Interest Calculator — the growth mechanics behind the formula
- Simple Interest Calculator — flat-rate comparison
- Financial Calculators — the full finance toolset
Frequently Asked Questions
What is the EMI formula?
EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where r is the monthly rate as a decimal and n is the number of monthly instalments.
Why is my early EMI mostly interest?
Interest is charged on the outstanding balance, which is highest at the start. As the balance falls, the interest portion of the fixed instalment falls and the principal portion grows.
Does a longer tenure reduce the cost of a loan?
No. It reduces the monthly instalment but increases total interest, because the balance stays high for longer.
How do I calculate EMI in a spreadsheet?
Use =PMT(rate/12, years*12, -principal). It implements the same formula.
What happens to my EMI if the interest rate changes?
On a floating-rate loan, lenders typically keep the EMI constant and extend the tenure, or reset the EMI at the reset date. Ask which approach your lender applies.
Summary
EMI is a single formula applied to three inputs: principal, monthly rate and number of instalments. Calculate the instalment, then always calculate total interest alongside it — that second number is what actually differs between offers. Run your own figures on the EMI Calculator.