How EMI is calculated — with a worked example

An EMI — equated monthly instalment — is the fixed amount you pay every month on a loan until it is cleared. It is the same every month, but what it pays for changes completely over the life of the loan.

The formula

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

• P is the amount borrowed;
• r is the monthly interest rate — the annual rate ÷ 12 ÷ 100;
• n is the number of monthly payments.

The formula finds the one payment that, repeated n times, covers each month's interest and leaves the balance at exactly zero at the end.

A worked example

Borrowing 500,000 for 5 years at 9% a year:

1. Monthly rate r = 9 ÷ 12 ÷ 100 = 0.0075.
2. Number of payments n = 5 × 12 = 60.
3. EMI = 500,000 × 0.0075 × 1.0075⁶⁰ ÷ (1.0075⁶⁰ − 1) = 10,379.18 a month.

Over 60 payments you repay 622,750.59 in total, of which 122,750.59 is interest. The EMI Calculator shows these figures and a full month-by-month schedule.

Why early payments are mostly interest

Interest is charged on what you still owe, and at the start you owe everything. In the first month of the example the interest is 500,000 × 0.0075 = 3,750, so only 6,629.18 of the 10,379.18 payment reduces the loan. Each month the balance is a little lower, the interest a little smaller, and more of the payment goes to the loan itself. The schedule shows that shift row by row.

Three rows from the same loan show how far it moves:

• Month 1: 3,750 interest, 6,629 off the loan.
• Month 30: about 2,146 interest, 8,233 off the loan.
• Month 60: about 77 interest, 10,302 off the loan.

After the first twelve payments you have paid about 124,550, but the balance has only fallen by about 82,915, to roughly 417,085. The other 41,635 was interest. This is why a loan feels as though it barely moves in its first year.

What a longer tenure really costs

Stretching the same 500,000 loan at 9% over more years lowers the payment but raises the total:

The 20-year loan costs more in interest than the amount borrowed. A lower EMI is easier month to month, but you pay for that comfort.

What one percentage point costs

The rate matters as much as the tenure. The same 500,000 over five years:

• at 8%: about 10,138 a month, about 108,300 in interest;
• at 9%: 10,379.18 a month, about 122,750 in interest;
• at 10%: about 10,624 a month, about 137,400 in interest.

Each point adds roughly 240 to the monthly payment and about 14,500 to the total over five years. On a twenty-year loan the same one-point difference is far larger, because the money is borrowed for four times as long — which is why it is worth comparing lenders carefully on long loans.

Paying extra: what prepayment does

Any payment beyond the EMI goes entirely to the loan, because the interest for that month has already been covered. That reduces every later month's interest. Two examples on the same loan, worked out with a simple month-by-month model:

• An extra 1,000 every month clears the loan in 54 months instead of 60 and saves about 13,900 in interest.
• A single extra payment of 50,000 at the end of the first year, with the EMI left unchanged, also clears it in 54 months and saves about 20,000.

The one-off payment saves more because it arrives early, when the balance and the interest are highest. After a prepayment, lenders usually let you choose between a shorter tenure and a lower EMI; keeping the EMI and shortening the tenure saves the most interest. Check the loan agreement first, because some loans charge a fee for early repayment.

Flat rate and reducing balance are not the same

Everything above assumes a reducing-balance loan, where interest is charged only on what you still owe. Some loans are quoted at a flat rate instead: interest is charged on the full original amount for the whole term, however much you have repaid.

At a flat 9%, the same loan costs 500,000 × 9% × 5 = 225,000 in interest, making the instalment 725,000 ÷ 60 = 12,083.33 a month. That is the payment a reducing-balance loan would charge at about 15.7%. A flat rate always sounds cheaper than it is, so when you compare offers, ask which method the rate uses — or compare the total amount repaid, which cannot be disguised.

Fixed and floating rates

On a fixed-rate loan the EMI is set at the start and stays there. On a floating-rate loan the rate moves with the market. When it rises, the lender either raises the EMI or, more often, keeps the EMI and lengthens the tenure — which can quietly add years to a long loan. If your rate changes, recalculate with the new rate and the outstanding balance to see what it has done to the end date.

Why your bank's figure may differ

Lenders add processing fees and insurance, and use their own rounding and day-count rules, so treat a calculator as a close estimate rather than a quote. This is a general illustration, not financial advice — always check the figures with the lender before you commit.

Related calculators

If you repay weekly or fortnightly rather than monthly, the Loan Calculator compares payment frequencies. For a home loan, the Mortgage Calculator adds property tax and insurance to the monthly figure. And to see the same compounding working in your favour, the Compound Interest Calculator projects how savings grow with regular contributions.