How EMI Is Calculated: Formula, Interest and Principal
The reducing-balance EMI formula step by step, how each instalment splits into interest and principal, and why a flat rate costs more, with a full worked example.
Published 28 October 2026
The short answer
EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), where r is the yearly rate ÷ 12 ÷ 100 and n the number of months. A ৳5,00,000 loan at 9% for 5 years costs ৳10,379 a month and ৳1,22,751 in interest; the same 9% as a flat rate costs ৳12,083 a month.
What an EMI is, and the formula
An EMI (equated monthly instalment) is the same amount you pay every month until a loan is fully repaid. With the standard reducing-balance method, each month’s interest is charged only on what you still owe. Every instalment first pays that month’s interest, and the rest reduces the principal (the amount borrowed).
EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)
- P = the loan amount (principal).
- r = the monthly interest rate as a fraction: yearly rate ÷ 12 ÷ 100.
- n = the number of monthly instalments (years × 12).
At 0% interest the formula simplifies to EMI = P ÷ n. To see the answer for your own loan straight away, use the EMI / Loan Calculator. Below, the same sum is worked by hand.
Worked example: ৳5,00,000 at 9% a year for 5 years
- Monthly rate: r = 9 ÷ 12 ÷ 100 = 0.0075, that is 0.75% a month.
- Number of instalments: n = 5 × 12 = 60.
- (1 + r)ⁿ = 1.0075⁶⁰ ≈ 1.565681.
- EMI = 5,00,000 × 0.0075 × 1.565681 ÷ (1.565681 − 1) = 3,750 × 1.565681 ÷ 0.565681 ≈ ৳10,379.18.
- Total payment = 10,379.18 × 60 ≈ ৳6,22,751.
- Total interest = 6,22,751 − 5,00,000 ≈ ৳1,22,751.
So about 19.7% of everything you pay over the 5 years is interest. Rounded, the instalment is ৳10,379 a month.
How each instalment splits into interest and principal
Each month, interest is worked out on the balance first, and the rest of the EMI reduces the principal:
- Month 1 interest: 5,00,000 × 0.0075 = ৳3,750.
- Month 1 principal repaid: 10,379.18 − 3,750 = ৳6,629.18.
- Balance left: 5,00,000 − 6,629.18 = ৳4,93,370.82.
- Month 2 interest: 4,93,370.82 × 0.0075 ≈ ৳3,700.28, so about ৳6,678.90 goes to principal.
The instalment stays the same, but each month the interest part shrinks a little and the principal part grows. In the last (60th) instalment the interest is only about ৳77.26. Added up by year:
| Year | Principal repaid (৳) | Interest (৳) | Balance at year end (৳) |
|---|---|---|---|
| 1 | 82,915 | 41,635 | 4,17,085 |
| 2 | 90,693 | 33,857 | 3,26,392 |
| 3 | 99,201 | 25,349 | 2,27,191 |
| 4 | 1,08,506 | 16,044 | 1,18,685 |
| 5 | 1,18,685 | 5,865 | 0 |
Each figure is rounded to the nearest Taka, so the interest column adds up to ৳1,22,750, ৳1 short of the total interest. In year 1 just over a third of what you pay is interest; in year 5 it is under 5%.
Flat rate vs reducing balance
With a flat rate, interest is charged on the original loan amount for the whole tenure, however much you have repaid. The principal and total interest are then added and divided by the number of instalments. With a reducing balance, interest is charged only on what is left. So the same percentage on paper costs much more as a flat rate.
An illustrative comparison only (not any lender’s terms): the same ৳5,00,000 at 9% for 5 years. As a flat rate, interest = 5,00,000 × 9% × 5 = ৳2,25,000, and the instalment = (5,00,000 + 2,25,000) ÷ 60 ≈ ৳12,083.33.
| 9%, 5 years | Reducing balance | Flat rate |
|---|---|---|
| Monthly instalment | ৳10,379 | ৳12,083 |
| Total interest | ৳1,22,751 | ৳2,25,000 |
| Total payment | ৳6,22,751 | ৳7,25,000 |
The same “9%” as a flat rate costs about ৳1,02,249 more in interest. To get a ৳12,083 instalment on a reducing balance, the rate would have to be about 15.7% a year. When you compare offers, ask which method is used and the total amount payable, not just the percentage.
Step by step: work out your own EMI
- Take the loan amount (P), interest rate and tenure from your loan offer.
- If the rate is yearly, divide by 12 and by 100 to get r; if it is monthly, divide by 100 only.
- Turn the tenure into months: n = years × 12.
- Work out (1 + r)ⁿ, then put it into the formula to get the EMI.
- Total payment = EMI × n, and total interest = total payment − P.
- Any month’s interest = the balance at that point × r; the EMI minus that is the principal repaid.
The same formula shows what a different tenure does. Over 3 years, the loan above has an EMI of about ৳15,900 and total interest of about ৳72,395; over 7 years, the EMI falls to about ৳8,045 but total interest rises to about ৳1,75,741. A longer tenure lowers the instalment and raises the total interest.
Common mistakes
- Mixing up flat and reducing rates. “9% interest” means two very different costs under the two methods, as the comparison above shows.
- Mixing up yearly and monthly rates. 9% a year is 0.75% a month. A rate of 1% a month is the same as 12% a year, not 1% a year.
- Treating the quoted rate as the effective yearly rate. 9% a year compounded monthly works out to an effective rate of about 9.38%.
- Forgetting fees and insurance. Processing fees, insurance and other charges are not part of the EMI formula. Add them separately to see the real cost, and ask the lender for the total amount payable.
- Expecting your bank’s schedule to match exactly. A lender’s actual schedule can differ a little because of how it rounds instalments, counts days, sets the first instalment date or changes a floating rate.
- Looking only at the instalment. The EMI comes out of your take-home pay. Check your net salary with the Salary Calculator first, then decide what instalment you can comfortably afford.
Rather than working it by hand, enter your loan amount, rate and tenure in the EMI / Loan Calculator to see the monthly instalment, total interest, total payment and the year-by-year split of principal and interest together. For the final figures, always go by your loan agreement.