How EMI is calculated: the formula, a worked example and why early EMIs are mostly interest

What an EMI is

EMI stands for equated monthly instalment: a fixed amount you pay every month until a loan is repaid. Each instalment has two parts, interest for that month and a repayment of principal. The total stays the same, but the split between the two changes every month. The lender charges interest on the balance still owed, so as the balance falls, the interest part falls and more of the same payment reduces principal.

The formula

The standard formula is EMI = P x r x (1 + r)^n / ((1 + r)^n - 1), where P is the loan amount, r is the monthly interest rate (the annual rate divided by 12 and by 100), and n is the number of monthly instalments.

It is not arbitrary. Think of the loan as a promise to pay a level amount E for n months. Today, the value of those payments, discounted at the monthly rate, must equal what you borrowed. So P = E/(1+r) + E/(1+r)^2 + ... + E/(1+r)^n. That is a geometric series, which sums to E x (1 - (1+r)^-n) / r. Solving for E gives E = P x r / (1 - (1+r)^-n), and multiplying top and bottom by (1+r)^n gives the familiar form above. The formula assumes interest is calculated monthly on the reducing balance and that payments are made at the end of each month.

EMI is the level payment whose discounted value equals the loan amount.

Worked example: 10 lakh at 9 percent for 20 years

Take P = 10,00,000 (1,000,000), an annual rate of 9 percent, and a term of 20 years. Then r = 9 / 12 / 100 = 0.0075 and n = 240. Computing with a script gives an EMI of 8,997.26. Over 240 payments, you pay 21,59,342.29 in total, so the interest is 11,59,342.29, more than the amount borrowed.

Now the first month. Interest is 10,00,000 x 0.0075 = 7,500.00. The rest of the 8,997.26, which is 1,497.26, reduces principal, so the balance becomes 9,98,502.74. In month 2, interest is 7,488.77 and principal is 1,508.49. Over the whole first year the interest paid is 89,240.01 and the principal repaid is only 18,727.10, so about 82.6 percent of the first year's payments go to interest.

Notice the pattern. After five years (60 payments) the balance is still 8,87,070.49, so only about 11.3 percent of the loan has been repaid even though 25 percent of the time has passed. Principal repaid first exceeds interest in month 149.

Why early payments are mostly interest

Interest each month equals the outstanding balance multiplied by the monthly rate. At the start the balance is at its maximum, so the interest is at its maximum. The fixed EMI is split so that interest comes off first and only the remainder reduces principal. Because the remainder is small, the balance falls slowly. As it falls, interest shrinks and the remainder grows, so principal repayment accelerates. Plotted on a chart, the principal portion curves upward and the interest portion curves downward across the term, crossing at month 149 in this example.

This matters in practice. If you leave a loan or sell a property early, you will have paid a lot of interest and still owe most of the principal. It also explains why a prepayment made early saves more than the same prepayment made late.

Interest is calculated on what you still owe, so the earliest payments are the most interest-heavy.

The effect of tenure

A longer term lowers the monthly EMI but increases the total interest, sometimes by a lot. Using the same 10,00,000 at 9 percent:

Moving from 20 to 25 years lowers the EMI by 605.30 a month, yet adds 3,58,246.80 of interest. Moving from 20 to 15 years raises the EMI by 1,145.41 but saves 3,33,662.44. The right balance depends on your cash flow and other goals, not on a rule.

The effect of a prepayment

Suppose that in the same loan you make a one-time prepayment of 1,00,000 right after the 12th EMI and keep paying the same EMI. The interest in the first 12 months is unchanged, but the balance drops by 1,00,000 immediately, and every later month's interest is charged on a smaller amount. The loan closes in month 190 instead of month 240, 50 months earlier, and total interest falls from 11,59,342.29 to 8,05,352.04, a saving of 3,53,990.25. The other option is to keep the term and let the EMI drop; the interest saving is smaller, but the monthly relief is immediate.

Check your loan agreement for prepayment charges, and ask whether the lender reduces tenure or EMI by default. Rules differ by lender, loan type and country.

Check the numbers yourself

Use the EMI Calculator or Home Loan EMI Calculator on this site to reproduce any row above: enter 10,00,000, 9 percent and 20 years, and compare with the table. The Loan Prepayment Calculator shows the effect of extra payments, and the Loan Comparison Calculator puts two offers side by side. Small differences of a few paise can appear because lenders round the EMI to the nearest rupee and may compute interest by days instead of months. Your sanction letter and repayment schedule are the authority; a calculator is for understanding and comparing.

Frequently asked questions

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