How is EMI Calculated? Formula with a Worked Example
Understanding how EMI (Equated Monthly Instalment) is calculated can help you make better decisions when taking out loans. This post explains the formula and provides a step-by-step worked example.
What is EMI?
EMI stands for Equated Monthly Instalment. It's the fixed payment you make every month towards repaying a loan, which covers both principal and interest.
The EMI Calculation Formula
The standard formula to calculate EMI is:
EMI = [P × r × (1 + r)^n] / [(1 + r)^n – 1]Where:
- P = Principal loan amount
- r = Monthly interest rate (annual interest rate divided by 12 and by 100)
- n = Number of monthly payments (loan tenure in months)
Worked Example: Calculating EMI
Suppose you borrow a principal amount (P) of 100,000 units at an annual interest rate of 12% for 2 years (24 months).
Let's calculate the EMI step by step:
- Calculate the monthly interest rate (r):
- Annual rate = 12% per year
- Monthly rate (r) = 12 / 12 / 100 = 0.01
- Total number of payments (n):
- 2 years = 24 monthly instalments
- Plug values into the EMI formula:
- P = 100,000
- r = 0.01
- n = 24
EMI = [100,000 × 0.01 × (1 + 0.01)^24] / [(1 + 0.01)^24 – 1]Calculate (1 + 0.01)^24:
- (1 + 0.01)^24 ≈ 1.2697346
Calculate numerator:
- 100,000 × 0.01 × 1.2697346 = 1,269.7346
Calculate denominator:
- 1.2697346 – 1 = 0.2697346
So,
EMI = 1,269.7346 / 0.2697346 ≈ 4,707.35Your monthly EMI payment would be approximately 4,707.35 units every month for 24 months. Over the whole loan you repay about 112,976.40 units, of which about 12,976.40 is interest.
Calculate EMI Instantly Online
For fast EMI calculation, use our EMI Calculator. Simply plug in your loan amount, interest rate, and tenure to get your exact EMI in seconds. For mortgage-specific EMI, try the Mortgage Calculator.
Summary
The EMI depends mainly on the loan amount, tenure, and interest rate. The above formula and example show you each step in detail. You can use free online tools to double-check your calculations anytime.