How to Calculate EMI (and Why Your Lender’s Number Differs)

An EMI (Equated Monthly Instalment) is a payment that stays the same every month while its internal composition changes completely. That is the whole idea, and it is also why the arithmetic looks stranger than it is.

The formula is:

where P is the principal, r is the monthly interest rate as a decimal, and n is the number of monthly payments.

The two conversions that trip people up

Both of the inputs need converting before they go in, and both conversions are routinely got wrong.

The rate is quoted per year but applied per month, so divide by 12 and then by 100. A 9% annual rate becomes 9 ÷ 12 ÷ 100 = 0.0075. Not 0.09. Not 0.75. The number you want is small, and if your answer looks wildly too big this is usually why.

The tenure is quoted in years but counted in payments, so multiply by 12. Five years is n = 60.

A worked example, by hand

Take a loan of ₹5,00,000 at 9% per annum over 5 years.

• P = 500000
• r = 0.09 ÷ 12 = 0.0075
• n = 5 × 12 = 60

First compute (1 + r)ⁿ = 1.0075⁶⁰ = 1.565681.

Now the numerator: 500000 × 0.0075 × 1.565681 = 5871.30.

And the denominator: 1.565681 − 1 = 0.565681.

So EMI = 5871.30 ÷ 0.565681 = ₹10,379.00 per month.

Over 60 months that totals ₹6,22,740, of which ₹1,22,740 is interest, roughly a quarter of the amount borrowed, paid for the privilege of spreading it over five years.

Why the formula has that shape

It is worth understanding rather than memorising, because the shape explains the behaviour.

The lender is solving a present-value problem: find the constant payment whose discounted stream, over n months at rate r, exactly equals the amount handed over today. Each future payment is worth less than its face value, discounted by (1 + r) for every month you wait. Summing that geometric series and rearranging for the payment gives you the expression above. The (1 + r)ⁿ terms are the compounding; the subtraction of 1 in the denominator is what is left when the series collapses.

The practical consequence is that EMI is not linear in any of its inputs. Doubling the tenure does not halve the payment, and it more than doubles the interest.

The crossover point

In the example above, month one breaks down as:

• Interest: 500000 × 0.0075 = ₹3,750
• Principal: 10379 − 3750 = ₹6,629

By month 60 the interest component is under ₹80. The instalment never changed; the balance it was charged against collapsed. If you want to see the whole progression rather than the endpoints, the EMI calculator prints every row: and its optional extra-payment field shows exactly how much sooner that collapse happens if you pay down principal early.

This is also why prepayment is worth most early. A rupee of principal repaid in month three removes 57 months of future interest on that rupee. The same rupee in month 55 removes five months of it.

Four reasons the bank’s number is higher

A calculator gives you the pure instalment. A lender gives you the cost of the loan. These are different figures and the gap is not an error.

Processing and documentation fees

Typically 0.5% to 2% of the principal, often deducted from the disbursed amount rather than added to the EMI. You borrow ₹5,00,000 and receive ₹4,95,000, but repay on the full ₹5,00,000. That raises the effective rate without changing the quoted one.

Insurance bundled into the principal

Loan protection cover is frequently financed alongside the loan. It increases P, and therefore the EMI, while appearing nowhere in the interest rate.

Broken-period interest

If the loan is disbursed on the 20th and instalments run from the 1st, the lender charges interest for those intervening days separately, sometimes as a larger first payment, sometimes as a deduction at disbursal.

The rate being floating

A quoted EMI on a floating-rate loan is a snapshot. When the benchmark moves, most Indian lenders hold the instalment and extend the tenure instead, which is easy to miss because your bank statement looks unchanged while the loan quietly grows longer.

Flat rate versus reducing balance

This is the single most expensive misunderstanding in consumer lending, so it is worth being blunt about it.

A reducing balance rate charges interest on what you still owe. That is what the EMI formula assumes and what any regulated home or personal loan uses.

A flat rate charges interest on the original principal for the entire tenure, regardless of what you have repaid. On a 5-year loan, a 9% flat rate is roughly equivalent to a 16 to 17% reducing rate, nearly double.

The rough conversion is:

where n is the number of years. It is an approximation, but it is close enough to tell you whether an offer is competitive. If a lender will not state which basis they are quoting, that is itself informative.

Before you sign

1. Confirm the rate is reducing balance, not flat.
2. Ask for the total amount repayable, not just the EMI. It is a single number that captures every fee.
3. Check whether prepayment carries a penalty, and whether it shortens the tenure or reduces the instalment.
4. On a floating rate, ask what happens when the benchmark rises: does the EMI move, or the tenure?
5. Run the numbers yourself before the meeting, so you are checking their figure rather than receiving it.

That last point is the reason this site exists. The arithmetic is not difficult, but doing it in advance changes the conversation from "can I afford this instalment" to "is this priced fairly".