Why this is important: When you take a loan (home, car, personal), the Equated Monthly Instalment (EMI) tells you exactly how much you'll pay every month. Knowing the EMI helps you plan cash flow, compare loan offers, and decide the ideal loan amount and tenure.
What is EMI?
An EMI is the fixed monthly payment you make to repay a loan. Each EMI includes two parts: interest on the outstanding balance and a portion of the principal. Over time the interest portion falls and the principal portion rises.
EMI Formula (best and standard method)
The widely used EMI formula (monthly compounding) is:
EMI = P × r × (1 + r)^n
-------------------------
(1 + r)^n − 1
Where:
- P = Loan principal (loan amount)
- r = Monthly interest rate = (Annual rate % / 12) / 100
- n = Total number of monthly instalments = loan years × 12
Step-by-step worked example (digit-by-digit arithmetic)
Example: Loan amount P = ₹10,00,000 (10 lakh), Annual interest rate = 9% p.a., Tenure = 5 years.
Step 1 — Compute monthly rate r:
Annual rate = 9% → r = 9 / 12 / 100 = 0.09 / 12 = 0.0075
Step 2 — Compute n (months):
Tenure = 5 years → n = 5 × 12 = 60 months
Step 3 — Compute (1 + r)^n carefully:
1 + r = 1 + 0.0075 = 1.0075 (1.0075)^60 ≈ 1.5656810269415706 (we've raised 1.0075 to the 60th power)
Step 4 — Compute numerator = P × r × (1 + r)^n:
P × r = 1,000,000 × 0.0075 = 7,500.000000000000 Numerator = 7,500 × 1.5656810269415706 = 11,742.60770206178
Step 5 — Compute denominator = (1 + r)^n − 1:
Denominator = 1.5656810269415706 − 1 = 0.5656810269415706
Step 6 — EMI = numerator / denominator:
EMI = 11,742.60770206178 ÷ 0.5656810269415706 EMI ≈ 20,758.355226353873
Result: EMI ≈ ₹20,758.36 per month for a ₹10,00,000 loan at 9% p.a. for 5 years.
Quick comparisons — same loan, different tenures (all at 9% p.a.)
Loan principal P = ₹10,00,000; Annual rate = 9%.
| Tenure (years) | Months (n) | EMI (approx.) | Total Paid (EMI × n) | Total Interest Paid |
|---|---|---|---|---|
| 5 | 60 | ₹20,758.36 | ₹20,758.36 × 60 = ₹12,45,501.60 | ₹12,45,501.60 − ₹10,00,000 = ₹2,45,501.60 |
| 10 | 120 | ₹12,667.58 | ₹12,667.58 × 120 = ₹15,20,109.60 | ₹15,20,109.60 − ₹10,00,000 = ₹5,20,109.60 |
| 15 | 180 | ₹10,142.67 | ₹10,142.67 × 180 = ₹18,25,680.60 | ₹18,25,680.60 − ₹10,00,000 = ₹8,25,680.60 |
| 20 | 240 | ₹8,997.26 | ₹8,997.26 × 240 = ₹21,59,342.40 | ₹21,59,342.40 − ₹10,00,000 = ₹11,59,342.40 |
Observation: Lower tenure → higher EMI but much lower total interest paid. Longer tenure → lower EMI but much higher total interest.
Why the standard formula is the best way
- It accounts for monthly compounding and the reducing principal correctly.
- It gives an exact fixed EMI so you can budget every month.
- Works for any interest rate and tenure and is widely accepted by lenders and calculators.
- Use the EMI formula to compare loan offers (interest rate & processing fees).
- If possible, choose a shorter tenure to save on total interest — but ensure EMI fits your cash flow.
- Prepayment or part-payment reduces outstanding principal and future interest; check lender prepayment rules and charges.
Try our EMI Calculator
Prefer to test multiple loan amounts, tenures and rates quickly? Use our free EMI Calculator to see instant results and amortization breakdowns:
Frequently Asked Questions
Q: Can EMI change during the loan?
A: If you have a floating interest rate, EMI may change when the bank revises the rate. Alternatively, the bank can keep EMI constant and change tenure — check loan terms.
Q: How much of EMI is interest vs principal?
A: In initial months most of EMI goes to interest. Over time the principal portion increases. Use an amortization schedule to see month-by-month breakup.
Q: Should I pick a longer tenure to reduce EMI?
A: Only if needed for cashflow. Longer tenure reduces monthly burden but increases total interest substantially.
Disclaimer: Calculations are illustrative. Exact EMIs depend on lender rounding, fees, and compounding rules. Use the EMI Calculator linked above for precise values and amortization.