When you take a loan, your bank calculates a fixed monthly payment called EMI (Equated Monthly Instalment). But how exactly is it calculated? Let's break it down.
The EMI Formula
Banks use the reducing balance method with this formula:
EMI = P × r × (1 + r)^n / [(1 + r)^n – 1]
Where:
- P = Principal loan amount
- r = Monthly interest rate = Annual rate ÷ 12 ÷ 100
- n = Total number of months = Years × 12
Step-by-Step Worked Example
Scenario: Home loan of ₹30,00,000 at 9% p.a. for 20 years
- P = ₹30,00,000
- r = 9 ÷ 12 ÷ 100 = 0.0075 (monthly rate)
- n = 20 × 12 = 240 months
- EMI = 30,00,000 × 0.0075 × (1.0075)^240 / [(1.0075)^240 – 1]
- EMI ≈ ₹26,992/month
Total amount paid = ₹26,992 × 240 = ₹64,78,080
Total interest paid = ₹64,78,080 − ₹30,00,000 = ₹34,78,080
Why Does EMI Stay the Same but Interest Changes?
In the reducing balance method, each month's interest is calculated on the outstanding principal (not the original loan). So:
- Early months: Higher portion goes to interest, less to principal
- Later months: More goes to principal, less to interest
This is why prepaying a loan early saves much more interest than prepaying later.
How to Reduce Your EMI
- Negotiate a lower interest rate — even 0.5% less saves lakhs over 20 years
- Increase tenure — reduces monthly EMI but increases total interest paid
- Make a larger down payment — reduces principal P
- Prepay when possible — even ₹10,000 extra/year can cut years off your loan