How EMI Is Calculated: Formula With a Worked Example

What an EMI is

EMI stands for Equated Monthly Instalment. It is the fixed amount you pay every month to repay a loan, such as a home loan, car loan, personal loan or education loan. Each EMI has two parts: interest on the amount you still owe, and repayment of a portion of the principal.

The amount stays the same each month, but the split between interest and principal changes over time. Early EMIs are mostly interest; later EMIs are mostly principal.

This article is general information to help you understand the maths. It is not financial advice, and your lender's loan agreement is the final word on your EMI.

The EMI formula

For a loan with a fixed interest rate on a reducing balance, the standard formula is: EMI = P x r x (1 + r)^n / ((1 + r)^n - 1).

Here the monthly rate is used, not the annual rate. If your loan is at 12 percent per year, the monthly rate r is 12 / 12 / 100 = 0.01.

• P is the principal, the loan amount you borrow
• r is the monthly interest rate (annual rate divided by 12, then by 100)
• n is the number of monthly instalments (tenure in years multiplied by 12)

Worked example

Suppose you borrow Rs 1,00,000 at 12 percent per year for 1 year.

Step 1: P = 1,00,000, r = 0.01 and n = 12.

Step 2: Work out (1 + r)^n. That is 1.01 raised to the power 12, which is about 1.126825.

Step 3: Multiply P x r x 1.126825. That is 1,00,000 x 0.01 x 1.126825 = 1,126.825.

Step 4: Divide by (1.126825 - 1) = 0.126825. So EMI = 1,126.825 / 0.126825, which is about Rs 8,884.88.

Over 12 months you pay about Rs 1,06,618.55 in total. The total interest is therefore about Rs 6,618.55.

How each EMI is split

In the first month, interest is charged on the full Rs 1,00,000. At 1 percent per month, that is Rs 1,000. The rest of the EMI, Rs 7,884.88, reduces the principal. Your outstanding balance becomes Rs 92,115.12.

In the second month, interest is 1 percent of Rs 92,115.12, which is about Rs 921.15. So about Rs 7,963.73 goes towards principal. Each month the interest part shrinks and the principal part grows, until the balance reaches zero after the 12th EMI.

A month-by-month table showing this split is called an amortisation schedule. Most lenders can share one, and an EMI calculator can show it too.

What changes your EMI

Three inputs decide the EMI: loan amount, interest rate and tenure. A larger loan or a higher rate increases the EMI. A longer tenure reduces the EMI but usually increases the total interest you pay, sometimes by a large amount on long home loans.

Real loans can have other features that the basic formula does not cover, such as processing fees, insurance bundled with the loan, floating rates that change over time, or part-prepayments. When a floating rate changes, lenders may change the EMI, the tenure or both.

• Higher loan amount: higher EMI
• Higher interest rate: higher EMI and higher total interest
• Longer tenure: lower EMI but usually much higher total interest
• Prepayments: reduce the outstanding principal and future interest, subject to the lender's terms

Using an EMI calculator sensibly

Doing this by hand is useful once to understand it, but a calculator saves time when you compare options. The Filyzo EMI Calculator lets you change the amount, rate and tenure and see the EMI and total interest instantly.

A common mistake is to compare loans by EMI alone. Two loans can have similar EMIs but very different total costs because of tenure and fees. Compare the total amount payable as well, read the loan terms carefully, and speak to a qualified advisor if you are unsure which option suits you.