How to Calculate Your Loan EMI (Manually)
Understanding how your Equated Monthly Installment (EMI) is calculated can give you better control over your finances. Let's break it down.
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 x R x (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.
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