How Equated Monthly Installment (EMI) is Calculated: Mathematical Guide

The Equated Monthly Installment (EMI) for fixed-rate loans is computed using the standard compound reducing-balance formula: $$\text{EMI} = \frac{P \cdot r \cdot (1+r)^n}{(1+r)^n - 1}$$ Where: - **P** = Principal loan amount borrowed - **r** = Monthly interest rate (Annual Interest Rate $\div 12 \div 100$) - **n** = Loan tenure expressed in total months (Years $\times 12$)

Worked Example:
- Principal (P): ₹1,000,000 ($100,000)
- Annual Rate: 9.0% -> Monthly rate (r) = 9 / 12 / 100 = 0.0075
- Tenure (n): 5 Years = 60 Months

Calculation:
EMI = [1,000,000 * 0.0075 * (1 + 0.0075)^60] / [(1 + 0.0075)^60 - 1]
EMI = [7,500 * 1.56568] / [1.56568 - 1]
EMI = 11,742.61 / 0.56568 = ₹20,758 per month.

In the early months of a loan tenure, the outstanding principal balance is at its highest. Consequently, the interest portion constitutes the vast majority of each monthly installment. As the principal is progressively paid down, the monthly interest charge decreases, allowing a larger portion of each successive EMI payment to reduce the remaining principal. - **Early Tenure:** High interest proportion, slow principal reduction. - **Late Tenure:** Low interest proportion, rapid principal payoff.

Borrowers should exercise caution when comparing lenders: - **Reducing Balance (Standard):** Interest is computed only on the outstanding unpaid principal balance. - **Flat Interest Rate (Misleading):** Interest is calculated on the original full principal amount throughout the entire loan tenure, resulting in an effective real interest rate nearly double the advertised flat percentage.