EMI Calculation Formula

Understanding the mathematical formula behind Equated Monthly Installment (EMI) calculations is essential for borrowers in Canada and the US to grasp how their loan repayments are structured. This guide simplifies the EMI formula with practical examples.

Whether you’re managing a home loan in Toronto or a personal loan in Vancouver, knowing how EMI is calculated can help you plan your finances better. Use our free EMI calculator to apply the formula to your loans instantly.

The standard formula for calculating EMI is: EMI = P × r × (1 + r)^n / [(1 + r)^n - 1], where:

• P is the principal loan amount (the initial amount borrowed).
• r is the monthly interest rate (annual interest rate ÷ 12 ÷ 100).
• n is the number of monthly payments (loan tenure in years × 12).

This formula ensures a fixed monthly payment that covers both principal and interest, gradually reducing the loan balance to zero over the loan term.

Let’s break down each component of the EMI formula:

• Principal (P): The amount you borrow, such as $20,000 for a personal loan.
• Monthly Interest Rate (r): If the annual interest rate is 6%, the monthly rate is 6 ÷ 12 ÷ 100 = 0.005.
• Number of Payments (n): For a 3-year loan, this is 3 × 12 = 36 months.
• Compound Factor ((1 + r)^n): This accounts for the compounding of interest over the loan term, adjusted monthly.

The formula balances the principal and interest components, ensuring each EMI payment reduces the outstanding balance while covering the interest accrued.

Let’s calculate the EMI for a $20,000 loan at 6% annual interest over 3 years:

• Principal (P): $20,000
• Annual Interest Rate: 6% (so monthly rate r = 6 ÷ 12 ÷ 100 = 0.005)
• Tenure (n): 3 years = 36 months

Plugging these into the formula: EMI = 20,000 × 0.005 × (1 + 0.005)^36 / [(1 + 0.005)^36 - 1] results in an EMI of approximately $608.44. The total repayment over 3 years would be $21,903.84, with $1,903.84 in interest.

The chart below shows how the EMI ($608.44) for the $20,000 loan at 6% over 3 years is split between principal and interest over time.

Ready to calculate your EMI using this formula? Use our free EMI calculator to test scenarios for your loan in Canada or the US.