EMI Formula — Complete Derivation & Examples
The EMI formula calculates equal monthly payments for a loan. Understanding its derivation helps you verify loan terms and make informed borrowing decisions.
EMI Formula (Reducing Balance)
EMI = P × r × (1+r)^n / ((1+r)^n - 1)
Where:
- P = Principal loan amount
- r = Monthly interest rate (annual rate / 12 / 100)
- n = Total number of monthly installments
Step-by-Step:
- 1
Convert annual rate
r = Annual Rate / (12 × 100). E.g., 10% → 0.00833.
- 2
Calculate (1+r)^n
Raise (1+r) to the power of n months.
- 3
Apply formula
EMI = P × r × (1+r)^n / ((1+r)^n - 1).
Worked Examples:
Home loan
P: ₹50,00,000Rate: 8.5%Tenure: 20 years
Result: ₹43,391/month
r = 0.00708. n = 240. (1.00708)^240 = 5.455. EMI = 50L × 0.00708 × 5.455 / 4.455 = ₹43,391