How EMI is calculated: formula, interest and prepayment

By Zulu Calculator · Updated 19 October 2026 · Money

An EMI (equated monthly instalment) is the same payment every month until a loan is repaid. It is worked out with one formula: EMI = loan × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), where r is the yearly rate ÷ 12 ÷ 100 and n is the number of months. A loan of 1,000,000 at 10% a year for 5 years has an EMI of 21,247.04, and you pay 274,822.68 in interest over the 60 months.

This guide explains the formula, why early EMIs are mostly interest, how the rate and the term change what you pay, flat versus reducing rates, and what part-payments really save. To skip the maths, use the EMI calculator with your own loan.

How is EMI calculated?

You need three numbers: the loan amount, the yearly interest rate and the term in months. Turn the yearly rate into a monthly one, then put everything into the formula.

monthly rate (r) = yearly rate ÷ 12 ÷ 100
number of months (n) = years × 12
EMI = loan × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)
interest this month = balance left × r
principal this month = EMI − interest this month

The EMI stays the same each month, but what it is made of changes. Each month the interest is worked out on the balance you still owe, the EMI pays that interest first, and whatever is left pays off the loan. This is called a reducing-balance loan, and it is how bank home and personal loans normally work.

The formula assumes a fixed rate for the whole term and that the first EMI is paid a month after you get the loan. Your lender's figures may differ slightly because of rounding, interest for the days before the first EMI (sometimes called broken-period interest) or the date of the first payment.

Why are early EMIs mostly interest?

Because interest is charged on the balance, and the balance is highest at the start. As you pay the loan down, the interest part shrinks and the principal part grows, even though the EMI never changes. Spreading a loan out like this is called amortization, and the table of every payment is an amortization schedule.

Here is the first year of the 1,000,000 loan at 10% for 5 years. The EMI is 21,247.04 every month.

First 12 EMIs on 1,000,000 at 10% for 5 years

In the first year you pay 92,696.42 of interest and only reduce the loan by 162,268.12. By the last EMI the interest part is just 175.60. On longer loans the effect is much stronger: on a 20-year loan at 9%, about 83% of what you pay in the first year is interest (see Example 2 below). The amortization calculator shows every payment for your own loan.

How do the rate and tenure change the EMI and total interest?

A longer term lowers the EMI, but you pay interest for more months on a balance that falls more slowly, so the total interest rises sharply. A higher rate raises both. This table is for a loan of 1,000,000:

EMI and total interest on a loan of 1,000,000

Two things stand out. Going from 10 to 20 years at 10% cuts the EMI by only about 27% (13,215.07 to 9,650.22) but more than doubles the interest. And over 20 years, even a 2-point difference in the rate changes the interest by more than 300,000. The shortest term you can pay comfortably is usually the cheapest choice, and it is worth comparing lenders even for a small cut in the rate.

What is the difference between a flat rate and a reducing rate?

With a reducing rate, interest is charged only on the balance you still owe, as in the tables above. With a flat rate, interest is charged on the full loan for the whole term, even though you repay part of it every month. Some car, bike and gadget loans quote a flat rate.

flat-rate interest = loan × flat rate ÷ 100 × years
flat-rate EMI = (loan + flat-rate interest) ÷ months

On 1,000,000 at 10% flat for 5 years, the interest is 1,000,000 × 0.10 × 5 = 500,000, and the EMI is 1,500,000 ÷ 60 = 25,000. At 10% on a reducing balance, the same loan costs 21,247.04 a month and 274,822.68 in interest. The flat-rate EMI of 25,000 is the same as paying about 17.27% a year on a reducing balance. So a flat rate is far dearer than it sounds. Advanced mode in the EMI calculator shows this true rate.

Worked examples

Example 1: 1,000,000 at 10% for 5 years

• Monthly rate: 10 ÷ 12 ÷ 100 = 0.008333
• Number of EMIs: 5 × 12 = 60
• (1.008333)⁶⁰ = 1.6453
• EMI: 1,000,000 × 0.008333 × 1.6453 ÷ 0.6453 = 21,247.04 (worked with the unrounded figures)
• First month's interest: 1,000,000 × 0.008333 = 8,333.33, so 21,247.04 − 8,333.33 = 12,913.71 pays off the loan
• Total interest over 60 months: 274,822.68, so you repay 1,274,822.68 in all

Example 2: a home loan of 5,000,000 at 9% for 20 years

• Monthly rate: 9 ÷ 12 ÷ 100 = 0.0075
• Number of EMIs: 20 × 12 = 240
• (1.0075)²⁴⁰ = 6.0092
• EMI: 5,000,000 × 0.0075 × 6.0092 ÷ 5.0092 = 44,986.30 (worked with the unrounded figures)
• First month's interest: 5,000,000 × 0.0075 = 37,500.00, so only 7,486.30 of the first EMI pays off the loan
• First year: your 12 EMIs pay 446,200.06 of interest and only 93,635.52 of principal
• Total interest over 20 years: 5,796,711.47, more than the loan itself

After 10 years (half the term) you still owe 3,551,294.49, about 71% of the loan. Over 15 years instead, the EMI rises to 50,713.33 but the total interest falls to 4,128,399.26. At 8.5% for 20 years, the EMI is 43,391.16 and the total interest is 5,413,878.80, so half a point less saves 382,832.67.

Example 3: a part-payment of 50,000 with the 12th EMI

Take the loan from Example 1. After the 12th EMI you still owe 837,731.88. You pay an extra 50,000, so the balance drops to 787,731.88. You can then ask the lender to do one of two things:

• Keep the EMI at 21,247.04 and finish sooner. The loan ends after 57 EMIs instead of 60. Total interest falls to 251,138.29, a saving of 23,684.39.
• Keep the end date and lower the EMI. The EMI drops to 19,978.92 for the remaining 48 months. Total interest falls to 263,952.48, a saving of 10,870.20.

Should I reduce my EMI or my tenure after a prepayment?

A part-payment (prepayment) goes straight to the balance, so less interest builds up from then on. What happens next depends on the choice you make:

• Reduce the tenure (same EMI, finish sooner). This saves the most interest, as Example 3 shows: 23,684.39 against 10,870.20.
• Reduce the EMI (same end date). This saves less, but frees up cash every month. It can make sense if your budget is tight.

Regular part-payments add up fast on long loans. On the 5,000,000 home loan from Example 2, an extra 100,000 paid once a year (with every 12th EMI) and the EMI kept the same clears the loan in 167 months, which is 13 years and 11 months instead of 20 years. You part-pay 1,300,000 in all and save 2,017,584.96 in interest. If you lower the EMI after each part-payment instead, you save 1,023,397.21 and the EMI falls to 7,147.18 by the end.

Part-payments early in the loan save the most, because that is when the balance is highest. Small regular extra payments started early often save more than one large payment late in the loan. The EMI calculator handles extra monthly, yearly and one-off part-payments for reducing-rate loans.

Check your loan agreement for any prepayment charge first. In India, under the RBI (Pre-payment Charges on Loans) Directions, 2025, banks and NBFCs can't charge individuals for prepaying a floating-rate loan taken for non-business purposes, for loans sanctioned or renewed from 1 January 2026. Fixed-rate loans may still carry a charge.

What else changes the real cost of a loan?

• Processing fees. You receive less money but repay the same EMI, so the true yearly rate (APR) is higher than the quoted rate. A 1% fee (10,000) on 1,000,000 at 10% for 5 years means you receive 990,000 but still pay 21,247.04 a month: an APR of about 10.43%, and a total cost of 284,822.68 with the fee. In India, lenders usually add 18% GST to the fee.
• EMI in advance. Some loans take the first EMI on day one. The EMI is then the normal EMI ÷ (1 + monthly rate): 21,071.45 instead of 21,247.04 on the Example 1 loan, with 264,286.96 of interest.
• Payments other than monthly. For loans paid weekly, every two weeks or quarterly, or loans with a balloon at the end, the loan calculator uses the same idea with the rate per payment instead of the monthly rate.

Common mistakes

• Choosing the longest term because the EMI is lowest. A lower EMI over a longer term almost always means much more interest in total.
• Comparing a flat rate with a reducing rate. 10% flat is not 10%. Over 5 years it costs about the same as 17.27% on a reducing balance.
• Forgetting the processing fee. Compare loans on the true yearly rate with fees, not just the quoted rate.
• Dividing the yearly rate by 12 and stopping there. The monthly rate is only part of the formula; interest each month is on the balance left, not the original loan.
• Expecting early EMIs to pay off much of the loan. On long loans the balance falls slowly for years. Check how much you still owe before you plan to sell or refinance.
• Lowering the EMI by default after a part-payment. Many people accept a lower EMI without asking. Keeping the EMI and finishing sooner saves more.
• Expecting your bank's figures to match to the last unit. Rounding, broken-period interest and the first payment date can make small differences.

What to do before you take or prepay a loan

1. Ask for the full terms in writing: the rate, whether it is flat or reducing, fixed or floating, the fee, and any prepayment charge.
2. Work out the EMI and total interest for two or three terms, and pick the shortest one you can pay comfortably. Many lenders like your EMIs to stay under about 40–50% of your take-home pay; Advanced mode in the EMI calculator shows your share.
3. Compare offers on the true yearly rate with fees included, not on the EMI alone.
4. When you prepay, tell the lender in writing whether you want a shorter term or a lower EMI, and ask for the new schedule.

This guide is general information to help you understand the maths, not financial advice for your situation.

Quick summary

• EMI = loan × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), with r = yearly rate ÷ 12 ÷ 100.
• Each EMI pays that month's interest first; the rest reduces the loan.
• Early EMIs are mostly interest, especially on long loans.
• A longer term lowers the EMI but raises the total interest sharply.
• A flat rate is much dearer than the same reducing rate.
• After a part-payment, keeping the EMI and finishing sooner saves the most.

Work out your own numbers with the EMI calculator, see every payment with the amortization calculator, or try other payment frequencies, balloons and fees with the loan calculator.

Formulas and figures checked against the maths used by our EMI, amortization and loan calculators (checked 19 October 2026). The RBI prepayment note is as stated on our EMI calculator (rules checked 9 October 2026).

This guide explains the rules in plain English for planning. It is not legal, financial or flight-operations advice; check your contract, the official source linked above, your employer or your operator.