Key Takeaway: EMI = [P × r × (1+r)^n] / [(1+r)^n - 1], where P = principal, r = monthly rate, n = tenure in months. A ₹10L loan at 9% for 10 years = ₹12,668 EMI.
What is EMI?
EMI (Equated Monthly Installment) is a fixed payment you make every month to repay a loan. It includes: • Principal: Part of the loan amount • Interest: Cost of borrowing money In early years, EMI is mostly interest. In later years, EMI is mostly principal.
The EMI Formula
EMI = [P × r × (1+r)^n] / [(1+r)^n - 1] Where: • P = Principal loan amount • r = Monthly interest rate (annual rate ÷ 12 ÷ 100) • n = Loan tenure in months Example: Calculate EMI for ₹10,00,000 loan at 9% for 10 years Step 1: Convert annual rate to monthly r = 9 ÷ 12 ÷ 100 = 0.0075 Step 2: Calculate tenure in months n = 10 × 12 = 120 months Step 3: Apply formula EMI = [10,00,000 × 0.0075 × (1.0075)^120] / [(1.0075)^120 - 1] EMI = [10,00,000 × 0.0075 × 2.4514] / [2.4514 - 1] EMI = 18,385.5 / 1.4514 EMI = ₹12,668 **Total amount paid = ₹12,668 × 120 = ₹15,20,160** **Interest paid = ₹15,20,160 - ₹10,00,000 = ₹5,20,160**
Real-Life Examples
**Home Loan: ₹50 lakhs at 8.5% for 20 years** • P = 50,00,000 • r = 8.5 ÷ 12 ÷ 100 = 0.00708 • n = 20 × 12 = 240 • EMI = ₹43,391 • Total paid = ₹1.04 Crore • Interest = ₹54 lakhs **Car Loan: ₹8 lakhs at 10% for 5 years** • P = 8,00,000 • r = 10 ÷ 12 ÷ 100 = 0.00833 • n = 5 × 12 = 60 • EMI = ₹17,025 • Total paid = ₹10.21 lakhs • Interest = ₹2.21 lakhs **Personal Loan: ₹2 lakhs at 14% for 3 years** • P = 2,00,000 • r = 14 ÷ 12 ÷ 100 = 0.01167 • n = 3 × 12 = 36 • EMI = ₹6,830 • Total paid = ₹2.46 lakhs • Interest = ₹46,000
How EMI Changes with Tenure
Same loan (₹20L at 9%), different tenures: **5 years (60 months):** • EMI: ₹41,519 • Total interest: ₹4.91 lakhs **10 years (120 months):** • EMI: ₹25,337 • Total interest: ₹10.40 lakhs **15 years (180 months):** • EMI: ₹20,277 • Total interest: ₹16.50 lakhs **20 years (240 months):** • EMI: ₹17,996 • Total interest: ₹23.19 lakhs **Key insight:** Longer tenure = Lower EMI but MUCH higher total interest!
Interest vs Principal in Each EMI
In a ₹10L loan at 9% for 10 years (EMI ₹12,668): **Month 1:** • Interest: ₹7,500 (10,00,000 × 0.75%) • Principal: ₹5,168 • Outstanding: ₹9,94,832 **Month 60:** • Interest: ₹3,889 • Principal: ₹8,779 • Outstanding: ₹5,04,672 **Month 120 (last):** • Interest: ₹94 • Principal: ₹12,574 • Outstanding: ₹0 **Notice:** Early EMIs are 60% interest. Last EMIs are 99% principal!
Tips to Reduce EMI Burden
1. **Prepay Early:** Every ₹1 lakh prepaid in first 2 years saves ₹50-80K interest 2. **Choose Shorter Tenure:** If you can afford higher EMI, choose 10 years instead of 20 3. **Negotiate Rate:** 0.5% lower rate = ₹35K saved on ₹10L loan over 10 years 4. **Avoid Unnecessary Loans:** Personal loans at 14-18% are expensive. Use only for emergencies 5. **Check EMI-to-Income Ratio:** Keep total EMIs under 40% of monthly income for financial safety
When to Take a Loan?
**Good debt (worth taking):** • Home loan: Asset appreciates, tax benefits • Education loan: Increases earning potential • Business loan: Generates returns **Neutral debt:** • Car loan: Depreciating asset but necessary for some **Bad debt (avoid):** • Personal loan for vacation/wedding • Credit card debt at 36-48% interest • Loans for lifestyle products