How EMI Works: The Formula, a Worked Example and Tips

Whether you are buying a motorcycle, a laptop, a car or a house, you will probably hear the word EMI. It stands for equated monthly instalment: the fixed amount you pay the bank every month until the loan is finished. Knowing how that number is built helps you compare offers and avoid surprises.

What is inside one EMI?

Every EMI has two parts:

• Interest (or profit): the bank's charge for lending you money, worked out on the amount you still owe.
• Principal: the part that actually reduces your debt.

The total stays the same each month, but the split changes. In the early months most of your payment is interest. As the balance falls, interest shrinks and more of the same payment goes to principal.

The EMI formula

Most loans use the reducing-balance method, and the EMI is:

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

• P = the loan amount (principal).
• r = the monthly interest rate. Divide the yearly rate by 12, then by 100. A 12% yearly rate gives r = 0.01.
• n = the number of monthly instalments. A 2-year loan has n = 24.

You do not need to memorise it. The point is that the EMI depends on only three things: how much you borrow, the rate and the time.

A worked example

Say you borrow 500,000 at 12% a year for 2 years. (These numbers are only for practice.)

• P = 500,000
• r = 12 ÷ 12 ÷ 100 = 0.01
• n = 24

First work out (1.01)²⁴, which is about 1.26973. Then:

EMI = 500,000 × 0.01 × 1.26973 ÷ (1.26973 − 1) = about 23,537 a month.

We checked this by running the calculation on a computer, and the unrounded figure is 23,536.74. Over 24 months you pay 23,536.74 × 24 = about 564,882. So the cost of borrowing is roughly 64,882 on top of the 500,000 you received.

Where the first payment goes

In month 1 you owe the full 500,000, so interest is 500,000 × 1% = 5,000. The rest of the EMI, 23,537 − 5,000 = about 18,537, reduces the principal. Your balance becomes roughly 481,463.

In month 2, interest is charged on the smaller balance, so it is a little less than 5,000 and a little more goes to principal. This continues until the balance reaches zero at month 24. After 12 payments you have repaid about 235,000 of principal, and about 264,908 is still outstanding. Half the time has passed, but a bit more than half the principal remains. That is normal for a reducing-balance loan.

How the numbers change

Using the same 500,000 loan, small changes make a big difference to the total cost:

• Longer term, lower EMI, higher total cost. Stretching the loan makes each payment easier but you pay interest for more months.
• Higher rate, higher EMI. Even one or two extra percentage points add up over several years.
• Bigger down payment, smaller loan. Because the EMI scales with P, borrowing less cuts both the instalment and the interest.

As a second practice case, 1,000,000 at 15% for 3 years gives an EMI of about 34,665, a total of about 1,247,952 and interest of about 247,952.

Reducing balance versus flat rate

Some lenders and dealers advertise a flat rate. Here interest is calculated on the original loan amount for the whole term, even though you keep paying the balance down. A flat rate of 12% sounds the same as 12% reducing, but it is much more expensive in reality, because you pay interest on money you have already returned. If an offer does not say which method it uses, ask. When comparing, always ask for the total amount you will pay, not just the monthly figure.

Practical tips before you borrow

• Keep the EMI affordable. A common rule of thumb is to keep all loan payments under about one third of your monthly income, so a bill or a bad month does not break your budget.
• Add the extra costs. Processing fees, insurance, valuation and registration charges can raise the real cost. Ask for them in writing.
• Check early repayment rules. Some banks charge a fee if you pay off early. Others let you make part-payments, which saves interest.
• Compare at least three offers using the same loan amount and the same term.
• Understand Islamic financing. Products such as diminishing musharakah or murabaha are structured differently from conventional loans. The monthly figure can still look similar, but ask how the profit is calculated and what happens if you pay late.
• Never skip an instalment. Late payment charges and a poor credit record can make future borrowing harder.

Try it yourself

Use our EMI calculator to enter your own amount, rate and term, and see the monthly payment and total interest straight away. If you are wondering how much of your salary is left after tax before you plan a loan, read our salary tax guide.