Introduction
An EMI (Equated Monthly Instalment) is a fixed monthly payment that covers both interest and a portion of principal on a loan. Behind the single number on your statement is a standard mortgage-style amortization formula used by virtually every bank, NBFC, and credit union worldwide. This article walks through the formula, a step-by-step calculation, and a month-by-month example so you can verify any loan quote yourself.
Definition
EMI is the monthly payment a borrower makes to repay a loan over a fixed term at a fixed (or initial) interest rate. Each EMI is identical in size, but its split between interest and principal changes every month — early EMIs are mostly interest, later EMIs are mostly principal.
Why It Matters
Knowing the math behind your EMI lets you:
- Spot mis-quoted EMIs before signing.
- Compare loans with different rates and tenures on a true total-cost basis.
- Understand how much interest you save by prepaying early.
The same formula powers your home loan, car loan, personal loan, education loan, and most business term loans.
The EMI Formula
EMI = P × r × (1 + r)^n / ((1 + r)^n − 1)
Where:
| Symbol | Meaning |
|---|---|
| P | Loan principal (amount borrowed) |
| r | Monthly interest rate (annual rate ÷ 12, in decimal form) |
| n | Total number of monthly instalments (years × 12) |
Total interest paid = (EMI × n) − P.
Step-by-Step Calculation
Step 1 — Convert the annual rate to a monthly rate. 9% annual → 9 ÷ 12 = 0.75% per month → 0.0075 as a decimal.
Step 2 — Convert tenure to months. 20 years → 20 × 12 = 240 months.
Step 3 — Compute (1 + r)^n. (1.0075)^240 ≈ 6.0091.
Step 4 — Plug into the formula. Numerator: P × r × (1+r)^n Denominator: (1+r)^n − 1
Step 5 — Divide. That is your EMI.
Worked Example
A home loan of ₹50,00,000 at 9% per year for 20 years.
- r = 0.09 ÷ 12 = 0.0075
- n = 240
- (1.0075)^240 = 6.0091
EMI = 5,000,000 × 0.0075 × 6.0091 / (6.0091 − 1)
= 5,000,000 × 0.0075 × 6.0091 / 5.0091
= 225,341 / 5.0091
≈ ₹44,986
- Monthly EMI: ₹44,986
- Total paid over 20 years: 44,986 × 240 = ₹1,07,96,640
- Total interest: 1,07,96,640 − 50,00,000 = ₹57,96,640
You can replicate this exact result in the EMI Calculator.
How the EMI Splits Each Month
For the same loan, the first month's interest is principal × monthly rate = 50,00,000 × 0.0075 = ₹37,500. The principal portion is EMI − interest = 44,986 − 37,500 = ₹7,486.
| Month | Opening Balance | Interest | Principal | Closing Balance |
|---|---|---|---|---|
| 1 | 50,00,000 | 37,500 | 7,486 | 49,92,514 |
| 2 | 49,92,514 | 37,444 | 7,542 | 49,84,972 |
| 12 | 49,06,140 | 36,796 | 8,190 | 48,97,950 |
| 120 | 33,30,000 | 24,975 | 20,011 | 33,09,989 |
| 240 | 44,632 | 354 | 44,632 | 0 |
The proportion of interest falls every month; principal repayment accelerates.
Common Mistakes
- Forgetting to convert annual to monthly rate. Plugging 9 (or 0.09) directly into r produces nonsense.
- Mixing years and months in n. n must be months.
- Comparing two loans by EMI alone. A longer tenure produces a smaller EMI but much larger total interest.
- Ignoring processing fees. A 1% processing fee on a ₹50L loan is ₹50,000 — a real cost not captured in the EMI itself.
- Assuming the rate is fixed. Floating-rate loans recompute the EMI (or tenure) every time the benchmark moves.
Frequently Asked Questions
See FAQs below.
Related Calculators
Related Articles
- What Is EMI And How Is It Calculated?
- How Loan Interest Works: Simple vs Compound
- Fixed vs Variable Rate Loans
Conclusion
The EMI formula is the same whether you are borrowing ₹5 lakh or ₹5 crore. Learn the five steps once and you can validate any loan quote in under a minute — and see, line-by-line, exactly how much of your money is going to the bank as interest versus reducing your principal.
Educational content based on the standard amortization formula used by banks and NBFCs. Not personalized financial advice.