How EMI Is Calculated, Month by Month

An EMI (equated monthly instalment) is a fixed payment that does two jobs at once. Part of it pays the interest charged on what you owe this month, and the rest reduces what you owe. Because the amount owed falls every month, the interest part falls too, and the principal part grows. The total stays the same.

The formula

For ₹1,00,000 at 12% a year over 12 months: r = 12 ÷ 12 ÷ 100 = 0.01, and (1.01)¹² = 1.126825. So EMI = 1,00,000 × 0.01 × 1.126825 ÷ 0.126825 = ₹8,884.88.

The formula looks arbitrary, but it is just the one level payment that brings the balance to exactly zero after n months. You can check that by doing the months one at a time, which is what the bank's system does.

A 12-month loan, every month shown

Each month the interest is 1% of the balance at the start of the month. Whatever is left of the ₹8,884.88 goes to principal.

Figures rounded to the paisa for display; the calculation carries full precision, so a row may differ by a paisa if you add it up by hand.

Month 1: interest is 1% of ₹1,00,000 = ₹1,000, so ₹7,884.88 of the EMI reduces the loan to ₹92,115.12. Month 2: interest is 1% of ₹92,115.12 = ₹921.15, so a little more, ₹7,963.73, goes to principal. By month 12 the interest is under ₹88 and almost the whole EMI is principal. Total interest over the year is ₹6,618.55.

Why the first EMIs on a home loan are mostly interest

The same arithmetic on a long loan looks very different, because the balance stays high for years. Take ₹30 lakh at 8.5% for 20 years. The EMI is ₹26,034.70, and the monthly rate is 8.5 ÷ 12 ÷ 100 = 0.7083%.

More than four-fifths of the first EMI is interest. The principal part does grow every month, but slowly: it only overtakes the interest part in month 143, nearly 12 years in. The balance does not fall below ₹15 lakh, half the loan, until month 166.

A year-by-year view makes the shape clearer:

Over the full 240 months the interest comes to about ₹32.48 lakh, more than the loan. This is also why a prepayment in the early years saves so much: it removes principal that would otherwise have been charged interest for a decade or more. The prepayment calculator puts a number on it.

Finding the balance without the whole schedule

If you only want to know what you will owe after a certain number of EMIs, there is a direct formula:

For the ₹30 lakh loan after 60 EMIs, that gives ₹26,43,815, the same as the year-5 row above. It is handy for checking a loan statement or for working out a foreclosure amount before you call the bank.

When the rate changes

On a floating-rate loan the lender recalculates at each reset. If you keep the EMI, the number of months left is found by turning the formula around:

Suppose the ₹30 lakh loan's rate rose from 8.5% to 9.5% after five years. With ₹26,43,815 owed and the EMI kept at ₹26,034.70, the loan needs about 206.6 more months instead of 180, so 27 extra EMIs once the last part-month is rounded up. Raising the EMI instead to ₹27,607 keeps the original end date. If r × B is ever bigger than the EMI, the EMI no longer covers the interest and the loan would never end; RBI's rules on rate resets are meant to stop lenders stretching tenure that far without telling you.

Rounding and the last EMI

Lenders collect EMIs in whole rupees, so ₹8,884.88 becomes ₹8,885. Paying 12 paise extra each month clears the loan a fraction early, and the final instalment is adjusted to whatever is left: ₹8,883.46 in this case. On big loans the same effect can make the last EMI noticeably smaller than the others. This is normal and not an error.

Broken-period interest and pre-EMI

Your first EMI rarely falls exactly one month after the money is paid out. If a home loan is disbursed on the 10th and EMIs are due on the 5th, there are some odd days before the regular cycle starts. Lenders charge interest for those days separately, either collected upfront or added to the first EMI. On ₹30 lakh at 8.5%, 20 days of interest is about 30,00,000 × 8.5% × 20 ÷ 365 = ₹13,973.

For a flat under construction, the bank pays the builder in stages. Until the full loan is out, many borrowers pay only the interest on what has been disbursed so far, called pre-EMI. None of that reduces the principal, and full EMIs start only after the final disbursement.

Checking your lender's figures

Banks and NBFCs must attach a repayment (amortisation) schedule to the Key Facts Statement they give you before a retail loan. Put the same amount, rate and tenure into the EMI calculator and compare. The EMI should match to within a rupee or so. If it is well above, look for a flat rate, an insurance premium added to the principal, or a fee you were not told about. The flat vs reducing rate calculator will show if a quoted rate is flat.