What is an EMI?
An Equated Monthly Installment (EMI) is a fixed payment amount made by a borrower to a lender at a specified date each calendar month. EMIs are used to pay off both interest and principal each month so that over a specified number of years, the loan is paid off in full.
It's the simplest way to pay back your loan. It consists of two parts: the principal amount and the interest on the loan.
The EMI Formula
The mathematical formula to calculate EMI is:
EMI = [P × R × (1+R)^N] / [(1+R)^N-1]
Where:
- P (Principal): The principal loan amount.
- R (Rate): The monthly interest rate. (Note: if the annual interest rate is 12%, the monthly rate would be 12 / 12 / 100 = 0.01).
- N (Number of installments): The number of monthly installments (loan tenure in months).
Let's Calculate with an Example
Suppose you take a personal loan of ₹5,00,000 for 5 years (60 months) at an annual interest rate of 12%.
EMI = [5,00,000 x 0.01 x (1+0.01)^60] / [((1+0.01)^60)-1]
First, let's plug the values into the formula:
- P: 5,00,000
- R: 12% per annum, which is 1% per month (0.01)
- N: 5 years, which is 60 months
Understanding the Amortization Schedule
For the first EMI of ₹11,122, the interest and principal components are calculated as follows:
First Month Calculation:
- Outstanding Principal: ₹5,00,000
- Interest for the month (1% of outstanding): ₹5,000
- Principal paid (EMI - Interest): ₹11,122 - ₹5,000 = ₹6,122
- New Outstanding Principal: ₹5,00,000 - ₹6,122 = ₹4,93,878
Second Month Calculation:
- Outstanding Principal: ₹4,93,878
- Interest for the month (1% of outstanding): ₹4,938.78
- Principal paid (EMI - Interest): ₹11,122 - ₹4,938.78 = ₹6,183.22
- New Outstanding Principal: ₹4,93,878 - ₹6,183.22 = ₹4,87,694.78
This process continues until the loan is fully paid off. Notice how the interest component decreases and the principal component increases with each EMI.