EMI (Equated Monthly Installment) is calculated using a standard mathematical formula used by all banks and financial institutions for loans like personal loans, car loans, and home loans.
EMI Formula
EMI = \frac{P \times r \times (1+r)^n}{(1+r)^n – 1}
Meaning of Each Term
| Symbol | Meaning |
|---|---|
| P | Principal loan amount |
| r | Monthly interest rate (annual rate ÷ 12 ÷ 100) |
| n | Loan tenure in months |
| EMI | Monthly repayment amount |
Step-by-Step Method to Calculate EMI
Step 1: Convert Annual Interest to Monthly Rate
If your interest rate is 12% per year:
Monthly interest rate = 12 ÷ 12 ÷ 100 = 0.01
Step 2: Convert Tenure into Months
If loan duration is 5 years:
n = 5 × 12 = 60 months
Step 3: Apply the Formula
Now plug values into the formula:
- P = loan amount
- r = monthly interest rate
- n = total months
Then calculate EMI using the formula.
Example Calculation
Let’s assume:
- Loan amount (P) = 500,000
- Interest rate = 10% per year
- Tenure = 5 years (60 months)
Step 1:
Monthly rate = 10 ÷ 12 ÷ 100 = 0.00833
Step 2:
n = 60
Step 3:
Apply formula → EMI ≈ 10,624 (approx.)
How EMI Works Internally
EMI is based on the reducing balance method, meaning:
- Interest is charged on remaining loan balance
- Early EMI payments include more interest
- Later EMI payments include more principal
Simple EMI Breakdown Table
| Month | EMI | Interest Portion | Principal Portion | Remaining Loan |
|---|---|---|---|---|
| 1 | Fixed | High | Low | High |
| Mid | Fixed | Medium | Medium | Reducing |
| Last | Fixed | Low | High | Zero |
Important Insight
Even a small change in interest rate or tenure can significantly change EMI:
- Higher tenure → lower EMI but more total interest
- Lower tenure → higher EMI but less total interest
Summary
To calculate EMI:
- Convert interest rate into monthly rate
- Convert tenure into months
- Use EMI formula
- Understand reducing balance effect