EMI Formula

Finance Formula • Published on July 30, 2026 • Last updated July 30, 2026

Mathematical Equation

$$EMI = P \times r \times \frac{(1 + r)^n}{((1 + r)^n - 1)}$$

Variable Definitions

P

Principal loan amount borrowed

r

Monthly interest rate (Annual Rate / 12 / 100)

n

Total number of monthly installments (Tenure in years × 12)

Detailed Explanation

In-Depth Guide

Key Concept

An Equated Monthly Installment (EMI) is a fixed payment amount made by a borrower to a lender at a specified date each calendar month. The EMI is structured to pay off both the interest and the principal balance of a loan over a set period.

In the early stages of the loan, a larger portion of the monthly payment goes toward interest, while in later stages, more goes toward the principal. This amortization schedule helps borrowers plan their monthly budget and track their path to debt freedom.

How to Calculate: Step-by-Step

1. Identify the principal loan amount ($P$). 2. Convert the annual interest rate ($R$) to a monthly rate ($r$) by dividing it by 12 and then by 100 ($r = R / (12 \times 100)$). 3. Determine the loan tenure in months ($n = \text{years} \times 12$). 4. Calculate $(1 + r)^n$. 5. Multiply $P$ by $r$, then by $(1 + r)^n$, and divide the result by $((1 + r)^n - 1)$ to find the EMI.

Worked Calculation Example

Let's calculate the EMI for a home loan of $100,000 at an annual interest rate of 8% for a tenure of 15 years: - Principal ($P$) = $100,000 - Monthly Interest Rate ($r$) = 8% / 12 months = 0.6667% = 0.006667 - Number of installments ($n$) = 15 years × 12 months = 180 months - Calculate $(1 + r)^n$: $$(1 + 0.006667)^{180} \approx 3.3069$$ - Apply the EMI formula: $$EMI = 100,000 \times 0.006667 \times \frac{3.3069}{3.3069 - 1}$$ $$EMI = 666.7 \times 1.4335 \approx \$955.65\text{ per month}$$ - Total Repayment Amount = $955.65 × 180 = $172,017 - Total Interest Paid = $172,017 - $100,000 = $72,017

Common Use Cases

  • Home Loan repayment calculations
  • Car Loan and Personal Loan budgeting
  • Comparing loan repayment options from different lenders
  • Assessing eligibility for a mortgage based on monthly budget

Frequently Asked Questions

Generally, EMIs remain fixed. However, you can change them by making prepayments (which reduces the principal and either tenure or EMI) or by refinancing the loan at a different interest rate or tenure.

For fixed-rate loans, fluctuations do not affect the EMI. For floating-rate loans, an increase in interest rates usually increases the loan tenure while keeping the EMI constant, or increases the EMI if tenure extension is not possible.

In a flat rate loan, interest is calculated on the initial principal throughout the tenure. In a reducing rate loan, interest is calculated only on the outstanding principal, making reducing rate loans significantly cheaper.

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