EMI Calculation – Principal and Interest

How is EMI Calculated?

EMI, or Equated Monthly Installment, is a fixed payment amount paid by a borrower to a lender at a specified date each calendar month. Let’s dive into EMI calculation. EMI is calculated using the formula:

EMI = [P * r * (1+r)^n] / [(1+r)^n-1]

Where:

  • P is the principal loan amount
  • r is the monthly interest rate (annual rate / 12)
  • n is the number of EMI payments

This formula computes the fixed monthly payment required to fully repay a loan with interest over the specified loan tenure.

For example, let’s consider a loan of 5,00,000 with an annual interest rate of 8.5% and a loan tenure of 5 years:

P = 5,00,000
r = 0.085 / 12 = 0.0070833
n = 5 * 12 = 60

Using these numbers in the formula gives us:

EMI = [500000 * 0.0070833 * (1+0.0070833)^60] / [(1+0.0070833)^60-1] ≈ 10,258.26

So, the monthly EMI payment for this loan would be approximately 10,258.

Breakdown of EMI Payment – Principal and Interest

EMI payments consist of both principal and interest components. The formula for calculating the EMI’s principal and interest portions for a particular month is as follows:

Interest Component = Outstanding Loan Amount * Monthly Interest Rate
Principal Component = EMI - Interest Component

Where:

  • EMI is the equated monthly installment we calculated from formula
  • Outstanding Loan Amount is the remaining amount to be paid
  • Monthly Interest Rate is the annual interest rate divided by 12

Each month, as you make your EMI payment, the principal portion of the payment reduces the outstanding loan amount, and the remaining portion is the interest payment.

For the same example, 5,00,000 at an annual interest rate of 8.5% for a loan tenure of 5 years (60 months), the monthly interest rate would be 0.085 / 12 = 0.0070833:

Outstanding Loan Amount = 5,00,000
Monthly Interest Rate = 0.0070833

For the first month:

Interest Component = 500000 * 0.0070833 (outstanding loan amount * monthly interest rate) ≈ 3,541.67
Principal Component = 10,258.26 - 3,541.67 (EMI - interest component) ≈ 6,716.59

So, in the first month, your EMI payment of 10,258.26 consists of 6,716.59 towards the principal and 3,541.67 towards the interest.

For the second month:

Outstanding Loan Amount = 500000 - 6716.59 (First month principal component) = 4,93,283.41
Interest Component = 4,93,283.41 * 0.0070833 (outstanding loan amount * monthly interest rate) ≈ 3,494.074
Principal Component = 10,258.26 - 3,494.074 (EMI - interest component) ≈ 6764.19

The same procedure will be followed in the following months until the outstanding loan amount is entirely paid off.