How to Calculate EMI Manually (With Formula)

Whether taking a home loan, buying a car, or funding an education, borrowing is a common phase in personal finance. When you borrow from a bank, you agree to repay the loan through Equated Monthly Installments (EMIs).

An EMI is a fixed payment made by a borrower to a lender on a specified date each calendar month. The beauty of an EMI is that it combines both the interest payment and the principal repayment into a single, predictable monthly sum.

But how do banks arrive at this exact EMI figure? While online loan calculators are widely available, understanding the underlying algebra is crucial to decoding how your loan works. This guide details the standard EMI mathematical formula and walks you through a step-by-step manual calculation.

1. The Reducing Balance Method

Modern consumer loans (home, car, and personal loans) almost always use the Reducing Balance Method.

Under this method:

Interest is calculated monthly on the outstanding loan principal, not the original loan amount.
As you make payments each month, your outstanding principal shrinks.
Consequently, the interest portion of your EMI decreases every month, while the portion going towards principal repayment increases.

Even though the mix of interest and principal changes monthly, the total EMI amount remains completely fixed throughout the loan tenure.

2. The Mathematical EMI Formula

To calculate the EMI on a reducing balance loan, we use the following amortization formula:

The Formula:

EMI = [

P × r × (1 + r)ⁿ (1 + r)ⁿ - 1

]

Where:

P = Principal loan amount (the amount you borrow).
r = Monthly interest rate. Since bank interest rates are quoted annually, you must convert the annual rate to a monthly rate and divide by 100: r = (Annual Rate / 12) / 100
n = Loan tenure in months. For example, a 5-year loan has 5 × 12 = 60 months.

3. Step-by-Step Calculation Example

Let’s calculate the EMI manually for a representative personal or car loan:

Principal (P) = ₹10,00,000
Annual Interest Rate = 8.40% per annum
Tenure (n) = 5 Years (60 months)

Step 1: Calculate the monthly interest rate (r)

r = (8.40 / 12) / 100 = 0.70% = 0.007

Step 2: Calculate the compounding factor (1 + r)ⁿ

(1 + 0.007)⁶⁰ = (1.007)⁶⁰ ≈ 1.519967

Step 3: Plug the values into the EMI formula

EMI =

10,00,000 × 0.007 × 1.519967 1.519967 - 1

EMI =

10,639.77 0.519967

EMI ≈ ₹20,464

The Result:

Your monthly payment will be ₹20,464.

Total Amount Repaid: ₹20,464 × 60 months = ₹12,27,840
Total Interest Paid: ₹12,27,840 - ₹10,00,000 = ₹2,27,840

4. Excel & Google Sheets Formula

If you want to quickly build an amortization sheet, you don’t need to do the algebra manually. You can use the built-in PMT function:

=PMT(rate, nper, pv)

For our example, type this in a cell:

=PMT(8.4%/12, 60, -1000000)

8.4%/12 converts the annual rate to monthly.
60 is the total number of periods (months).
-1000000 is the present value (the negative sign formats the resulting payment as a positive number).

5. EMI vs. Recurring Savings

Understanding how EMI interest compounds in reverse helps you see the opportunity cost of borrowing. If you pay ₹20,464 per month in EMIs, that is cash flow that cannot be compounded for your own retirement.

If instead of paying ₹20,464 in loan EMIs you invested that same ₹20,464 monthly into a compound savings plan, your money would compound in your favor. You can see the math of monthly recurring payments compounding in your favor using our Recurring Deposit vs. Fixed Deposit Calculator.