How to Calculate Loan EMI: Formulas, Logic, and Repayments

Equated Monthly Installment (EMI) represents the flat monthly sum paid by a borrower to a lender to repay both the principal amount and accrued interest over a fixed timeline.

The Standard Amortization Formula

The mathematical formula used to calculate EMI is:

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

Where:

P = Principal (loan amount borrowed)

r = Monthly interest rate (Annual Rate / 12 / 100)

n = Tenure in months (Years * 12)

Example Calculation

Let's assume a loan profile with the following variables:

Principal (P): $100,000

Annual Rate: 12%

Tenure: 5 years (60 months)

Steps:

1. r = 12 / 12 / 100 = 0.01

2. n = 60

3. EMI = 100,000 * 0.01 * (1.01)^60 / ((1.01)^60 - 1)

4. Result: EMI = $2,224.44 per month

Amortization Breakdown

With each repayment:

A portion of your EMI goes toward reducing the accrued interest for the month.

The remainder goes toward bringing down the principal balance.

Over time, the interest share shrinks while the principal reduction share expands.