Understanding Loan EMI Calculations: The Math Behind the Monthly Payment

What is an EMI?

EMI stands for Equated Monthly Installment. It's the fixed amount you pay every month to repay a loan over a set period. Each payment covers two components: principal (the amount you originally borrowed) and interest (the lender's charge for lending you the money).

In the early years of a loan, most of your EMI goes to interest. In the later years, most of it goes to principal. This is called amortization.

The EMI formula

The monthly EMI is calculated using the formula: EMI = P × r × (1 + r)ⁿ / ((1 + r)ⁿ - 1), where P is the principal, r is the monthly interest rate (annual rate ÷ 12 ÷ 100), and n is the total number of monthly payments (years × 12).

This is sometimes called the "annuity formula" because it's the same math used to calculate any fixed periodic payment — pensions, insurance premiums, even car leases.

A worked example

Suppose you borrow $100,000 at 8% annual interest for 20 years (240 months). r = 0.08 / 12 = 0.00667. Plugging in: EMI = 100,000 × 0.00667 × (1.00667)²⁴⁰ / ((1.00667)²⁴⁰ - 1) ≈ $836.88.

Over 20 years, you'll pay $200,852 — almost double the original loan — with $100,852 going entirely to interest.

Why a longer loan costs more

Stretching the same $100,000 loan to 30 years drops the EMI to about $733.76 — but you'll pay $264,154 in total, with $164,154 of that being interest.

The lower monthly payment feels good, but the total cost is 31% higher. Always compare loans on total cost, not just monthly payment.

How to use the calculator

Our EMI calculator handles this math for you, with 128-digit BigNumber precision. Try entering different principal amounts, rates, and tenures to see how the total interest changes. The amortization schedule (year-by-year breakdown of principal vs. interest) makes it easy to see when you cross the halfway mark.