The EMI (Equated Monthly Instalment) formula calculates the fixed monthly payment required to repay a loan, combining both principal and interest, over a set tenure at a given interest rate. It's the standard formula behind home loans, personal loans, car loans, and any other fixed-tenure amortizing loan in India.
Formula
EMI = P Ć r Ć (1 + r)āæ / [(1 + r)āæ ā 1]
| Variable | Meaning |
|---|---|
| EMI | Fixed monthly payment |
| P | Loan principal (amount borrowed) |
| r | Monthly interest rate (annual rate Ć· 12 Ć· 100) |
| n | Loan tenure in months |
Worked Example
A ā¹50,00,000 home loan at 8.5% per annum for 20 years (240 months):
- Monthly rate: r = 8.5% Ć· 12 Ć· 100 = 0.00708
- EMI = 50,00,000 Ć 0.00708 Ć (1.00708)Ā²ā“ā° / [(1.00708)Ā²ā“ā° ā 1] = ā¹43,391
- Total repaid over 20 years: ā¹43,391 Ć 240 = ā¹1,04,13,879
- Total interest paid: ā¹1,04,13,879 ā ā¹50,00,000 = ā¹54,13,879
The total interest paid (ā¹54.14 lakh) actually exceeds the original loan amount (ā¹50 lakh) ā a common surprise with long-tenure home loans, where the compounding effect of interest over two decades adds up to more than the principal itself.
Key Things to Know
- Prepaying principal early reduces total interest disproportionately, because early-tenure payments carry the highest interest share. A prepayment in year 2 saves far more total interest than the same prepayment in year 18.
- A Fixed vs Floating Rate decision changes what 'r' actually does over time ā a fixed rate keeps r constant for the full formula, while a floating rate recalculates the EMI or tenure whenever the rate resets.
- This formula assumes equal monthly instalments. Some loans use a reducing-balance step-down structure instead, where the payment itself changes over time ā check your loan's actual repayment structure before assuming the standard EMI formula applies.
- The formula breaks down at r = 0% (a zero-interest loan), where EMI simplifies to just P Ć· n, since there's no interest component to compound.