How EMI Is Calculated (And What Prepayment Actually Saves)

An EMI — equated monthly instalment — is a single fixed payment that clears both interest and principal over a set number of months. "Equated" is the whole idea: the amount never changes, so you can budget around it. What changes, invisibly, is how much of each instalment the lender keeps as interest.

The formula

EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)

• P — principal, the amount actually borrowed
• r — the monthly interest rate as a decimal
• n — the total number of monthly instalments

The two conversions are where most errors occur. An 8.5% annual rate becomes 0.085 ÷ 12 = 0.00708333 per month, and a 20-year tenure becomes 20 × 12 = 240 instalments. Putting an annual rate or a number of years into the formula gives an answer that is wrong by an order of magnitude.

Worked example: a 25,00,000 loan at 8.5% for 20 years

Step by step:

1. P = 2,500,000
2. r = 0.085 ÷ 12 = 0.0070833333
3. n = 240
4. (1 + r)^n = 1.0070833333²⁴⁰ = 5.441243
5. Numerator: 2,500,000 × 0.0070833333 × 5.441243 = 96,355.68
6. Denominator: 5.441243 − 1 = 4.441243
7. EMI = 96,355.68 ÷ 4.441243 = 21,695.58

Over the full term you pay 240 × 21,695.58 = 52,06,939, of which 27,06,939 is interest. You borrowed 25 lakh and repaid more than double — and that is at a rate most borrowers would consider reasonable.

Where each instalment goes

Interest each month is charged on the balance outstanding that month, and the rest of the EMI reduces the principal.

In the first instalment, 81.6% goes to interest and only 3,987 touches the debt. Principal first exceeds interest at instalment 143 — nearly twelve years in. After five full years of payments, about 13 lakh has left your account and the balance has fallen by just 2,96,820, or 11.9% of the loan.

This is not a hidden charge. It is the unavoidable consequence of interest being charged on a balance that starts at its maximum.

What prepayment does

A prepayment lands entirely on the principal, so it cancels every future month of interest that principal would have generated.

• A lump sum of 5,00,000 at month 60: the tenure drops from 240 to 176

instalments — 64 months shorter — and total interest falls from 27,06,939 to 17,97,864, saving 9,09,075. A 20% prepayment removed a third of the interest.

• An extra 5,000 every month from the start: the loan closes at instalment

155 instead of 240, saving 10,89,360. Raising the payment by 23% cut the interest bill by 40%.

Timing is everything. The same rupee prepaid in year two cancels eighteen years of interest; prepaid in year eighteen it cancels two. Also confirm with your lender that a prepayment reduces the tenure rather than recalculating a lower EMI — tenure reduction saves more, and lenders often default to the other option.

Tenure versus EMI

The same 25,00,000 at 8.5%:

Notice the asymmetry. Going from 20 to 30 years cuts the EMI by 2,473 — about 11% — but adds 17,13,282 in interest. Long tenures buy affordability at a price that is easy to underestimate, because the saving is visible monthly and the cost is only visible in total.

Rate sensitivity

Half a percentage point is not a rounding error on a 20-year loan:

A 0.5% difference costs about 1.9 lakh over the term. On a floating-rate loan this is also what happens to you when the benchmark moves.

Reducing balance versus flat rate

The formula above is a reducing balance calculation: interest is charged only on what you still owe. Some products — more often short-term consumer and vehicle finance — quote a flat rate instead, charging interest on the original principal for the whole term.

On the same loan, a flat 8.5% would mean interest of 2,500,000 × 0.085 × 20 = 42,50,000, a total of 67,50,000, and an instalment of 67,50,000 ÷ 240 = 28,125. That is 6,429 a month more than the reducing balance EMI of 21,696, for an identically described "8.5%". A flat rate is always worse than the same reducing-balance rate, and the gap widens with tenure because you keep paying interest on principal you repaid years ago.

Whenever a lender quotes a monthly instalment and a rate that do not reconcile through the EMI formula, a flat rate is usually why.

What the formula assumes

• Interest compounds monthly at exactly 1/12 of the annual rate. Lenders that

accrue daily will differ by a few rupees a month.

• Every instalment arrives on time. A late payment leaves a larger balance

for the next accrual, so the final instalment adjusts.

• The rate never changes, which is only true of a genuinely fixed product.
• The loan starts the month it is disbursed. Pre-EMI interest during a

construction-linked disbursal is charged separately and is not part of n.

Common mistakes

• Comparing EMIs instead of total cost. A lower EMI over a longer tenure is

usually the more expensive loan.

• Forgetting processing fees and insurance, which are often deducted from the

disbursal, so you receive less than P while paying interest on all of it.

• Assuming a floating EMI is fixed. Many lenders hold the EMI constant and

extend the tenure when rates rise, which hides the increase until you look at the closing date.

• Ignoring part-prepayment limits or charges, which vary by product and are

worth checking before you commit.

This is arithmetic, not financial advice. Check your own figures with the EMI calculator, compare products with the loan calculator, and see the full month-by-month split in the amortization calculator.