What is an Equated Monthly Installment (EMI)?
An Equated Monthly Installment (EMI) is a fixed payment amount made by a borrower to a lender at a specified date each calendar month. EMIs are applied to both interest and principal each month so that over a specified number of years, the loan is paid off in full.
How Amortization Works
In the initial years of a long-term loan (such as a 20-year mortgage), a substantial portion of each monthly EMI goes toward servicing the accrued interest. As the principal balance reduces over time, a progressively greater fraction of each payment applies toward paying down the principal.
Mathematical Formula
Loan EMI Formula
The Equated Monthly Installment (EMI) is calculated using the following formula:
EMI = P × R × (1 + R)N / [(1 + R)N − 1]
Formula Variables
- P: Principal loan amount.
- R: Monthly interest rate, calculated as annual interest rate ÷ 12 ÷ 100.
- N: Total number of monthly installments (loan tenure in years × 12).
- EMI: Fixed monthly installment payable during the loan tenure.
Example Calculation
Suppose you borrow Rs. 500,000 at an annual interest rate of 12% for 5 years.
- Principal (P) = Rs. 500,000
- Monthly interest rate (R) = 12 ÷ 12 ÷ 100 = 0.01
- Total installments (N) = 5 × 12 = 60 months
- Estimated monthly EMI = Rs. 11,122
Note: This estimate excludes processing fees, insurance, taxes, and other lender charges. Actual payments may vary by lender and loan terms.
Step-by-Step Worked Example
For a loan of $100,000 at an annual interest rate of 6% for 10 years (120 months):
1. Monthly rate r = 6 / 12 / 100 = 0.005
2. (1 + 0.005)┬╣┬▓Ôü░ Ôëê 1.8194
3. EMI = [100,000 ├ù 0.005 ├ù 1.8194] / [1.8194 ÔêÆ 1] = 909.70 / 0.8194 Ôëê $1,110.21 / month
4. Total Payment over 10 years: $1,110.21 × 120 = $133,225.20 (Total Interest: $33,225.20).
Important Considerations & Limitations
This calculation assumes a fixed interest rate throughout the entire tenure. Variable or adjustable-rate loans (ARMs) will see payment amounts fluctuate when benchmark interest rates shift.
Authoritative References
Federal Reserve Board Consumer Handbook on Adjustable-Rate Mortgages.