How Banks Calculate EMI: Understanding the Formula and Method

When you take out a loan, banks use a specific method to calculate the Equated Monthly Installment (EMI). This method, known as the reducing balance approach, takes into account the principal loan amount, the interest rate, and the loan tenure to arrive at your monthly payment. While it might seem daunting, in this post, we’ll break down the process to help you understand how to calculate EMI.

Understanding the Reducing Balance Method

Banks don't charge simple interest on loans. Instead, they employ a mechanism known as the reducing balance method to calculate the EMI. This method is a bit more complex than simple interest and involves a formula that dynamically adjusts the interest component of your EMIs over time.

The EMI Formula

Here is the formula used by banks to calculate the EMI:

EMI P × R × 1 R^(N) / [1 R^(N) - 1]

Where:

P Principal loan amount (the initial amount borrowed) N Loan tenure in months R Monthly interest rate, calculated as Annual Rate of interest / 12 / 100

Example Calculation

Let's go through an example to see how this works in practice. Suppose you've taken a loan of Rs 1 lakh at an annual interest rate of 14% for 1 year. Here’s how you'd calculate the EMI:

Step 1: Calculate the Monthly Interest Rate

R 14 / (12 × 100) 0.01166667

Step 2: Determine the Total Number of Installments

N 1 year × 12 months 12 months

Step 3: Plug the Values into the EMI Formula

EMI 100,000 × 0.01166667 × 1 0.01166667^12 / [1 0.01166667^12 - 1]

Simplifying this gives us an EMI of Rs 7745.

Why the Formula Works

The formula accounts for the fact that each month, a portion of your EMI goes towards reducing your principal loan amount, thereby lowering the interest you owe. As your principal balance decreases, the interest charged each month also decreases. This is why the EMI formula is called the reducing balance method.

Understanding Interest Payment Over Time

Let's look at a more detailed example to understand the dynamics of interest payment over time:

Month Principal Amount Outstanding Interest Felt Principal Paid EMI 1 98,245.91 1,014.09 8,722.00 8,722.00 2 91,986.91 962.96 8,759.04 8,722.00 3 83,796.88 919.12 8,802.88 8,722.00 4 74,024.00 881.00 8,840.99 8,722.00 5 63,373.19 848.72 8,873.38 8,722.00 6 51,739.81 819.99 8,902.31 8,722.00 7 39,017.50 793.49 8,928.41 8,722.00 8 25,109.10 768.90 9,953.10 8,722.00 9 10,035.10 745.89 10,984.11 8,722.00 10 -4,964.90 0.00 13,686.91 8,722.00

As you can see, each EMI consists of both principal and interest components. Over time, the principal debt decreases, leading to a natural decrease in the interest amount.

What If a Bank Says "Simple Interest"?

It's important to note that all lenders calculate loans using the reducing balance method. If a bank claims that you'll pay 8% interest on a Rs 1 lakh loan, you will not pay exactly Rs 8000 in interest. The actual amount of interest you will pay will be calculated using the reducing balance method, as explained above. Simple interest, in such cases, would be a less accurate representation of your total interest obligations.

Conclusion

Banks use a proven and effective method to calculate the EMI for loans. The reducing balance method ensures that your payments are structured in a way that minimizes your overall cost while allowing you to gradually pay off your loan. Understanding the EMI formula can help you make more informed financial decisions and manage your debt more effectively.

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