Comprehensive Guide • Home loans

How Home Loan EMI is Calculated with Worked Examples

✍️ Author: AG World Tools Editorial Team ⚖️ Reviewed by: Verified by AG World Tools Technical & Financial Review Board 📅 Last Reviewed: 2026-11-01

A home loan Equated Monthly Instalment (EMI) is calculated using the reducing balance mathematical formula $E = P \times r \times \frac{(1+r)^n}{(1+r)^n - 1}$. In this formula, $P$ represents the loan principal, $r$ represents the periodic monthly interest rate, and $n$ represents the total repayment tenure in months.

Every monthly instalment you pay is divided into two distinct components: interest payable on the outstanding principal balance for that month, and principal repayment that reduces your remaining debt.

---

The Mathematical Formula Explained

$$\text{EMI} = P \times r \times \frac{(1+r)^n}{(1+r)^n - 1}$$

  • $P$ (Principal): The total loan amount borrowed from the bank or financial institution.

  • $r$ (Monthly Interest Rate): Annual interest rate divided by $12 \times 100$. For example, an 8.5% annual rate gives $r = 8.5 / 1200 = 0.0070833$.

  • $n$ (Tenure in Months): Number of years multiplied by 12. A 20-year loan has $n = 20 \times 12 = 240$ months.

    • ---

    Step-by-Step Worked Example

    Consider a borrower taking a home loan with the following parameters:

  • Principal ($P$): ₹50,00,000 (₹50 Lakh)

  • Annual Interest Rate: 8.50% per annum

  • Tenure ($n$): 20 Years (240 Months)

    • 1. Compute Monthly Interest Rate

    $$r = \frac{8.50}{12 \times 100} = 0.00708333$$

    2. Compute Growth Factor $(1 + r)^n$

    $$(1 + 0.00708333)^{240} \approx 5.41944$$

    3. Compute Monthly EMI

    $$\text{EMI} = 50,00,000 \times 0.00708333 \times \frac{5.41944}{5.41944 - 1}$$ $$\text{EMI} = 35,416.67 \times 1.22627 \approx \mathbf{₹43,391}$$

    ---

    First Month Payment Breakdown

    In Month 1:

  • Monthly Interest Accrued: $₹50,00,000 \times 0.00708333 = \mathbf{₹35,417}$

  • Principal Repayment: $₹43,391 - ₹35,417 = \mathbf{₹7,974}$

  • New Principal Balance: $₹50,00,000 - ₹7,974 = \mathbf{₹49,92,026}$

    • Notice that in the very first month, over 81% of your payment covers interest, while less than 19% reduces your loan debt. Over time, as the principal balance decreases, the monthly interest shrinks and the principal portion expands.

    ---

    Amortisation Summary Over 20 Years

  • Total Principal Borrowed: ₹50,00,000
  • Total Interest Payable: ₹54,13,879
  • Total Repayment Amount: ₹1,04,13,879

    • ---

    Frequently Asked Questions

    Why does my bank's EMI quote differ by a few rupees?

    Some commercial banks compute monthly rates based on 365 days rather than an even 12 months, or round up fractional paise to the nearest whole rupee. AG World Tools reconciles each period to zero paise.

    Can my EMI amount change during the tenure?

    Yes, if you hold a floating-rate home loan. When the RBI revises the repo rate, banks adjust their Repo Linked Lending Rate (RLLR). By default, banks increase or decrease the loan tenure while keeping the monthly EMI constant, unless requested otherwise.

    ⚡ Try the Interactive Tool

    Perform this exact calculation with your own numbers on our free, zero-upload tool.

    Open Home Loan EMI Calculator →

    Official Sources & Statutory References