How an EMI Is Calculated

How banks work out a fixed monthly instalment on a loan, why early payments are mostly interest, and how rate and tenure change the total you pay.

An EMI, or equated monthly instalment, is the fixed amount you pay each month on a loan until it is fully repaid. Each EMI contains two parts: interest on the amount still owed, and principal, which reduces the loan.

The formula

Banks use this formula:

EMI = P x r x (1 + r)^n / ((1 + r)^n - 1)

P is the loan amount.
r is the monthly interest rate (annual rate divided by 12, as a decimal).
n is the number of monthly payments.

You rarely need to calculate it by hand; online EMI calculators do it instantly. But understanding it helps.

An example

A home loan of 10 lakh rupees at 9 percent a year for 20 years:

r = 0.09 / 12 = 0.0075
n = 240 months
EMI works out to about 8,997 rupees.

Over 20 years, you pay about 8,997 x 240, or roughly 21.6 lakh rupees. That means about 11.6 lakh rupees in interest, more than the original loan.

Why early EMIs are mostly interest

Interest is charged on the outstanding balance. At the start, the balance is highest, so most of the EMI goes to interest. In the first month of the example, interest is 10 lakh x 0.0075 = 7,500 rupees, so only about 1,500 rupees reduces the principal. Over time, the balance falls, interest shrinks and more of each EMI goes to principal. The schedule showing this is called an amortisation schedule.

What changes the total

Higher rate: a higher EMI and more total interest.
Longer tenure: a lower EMI but much more total interest.
Shorter tenure: a higher EMI but far less total interest.

For the same 10 lakh loan at 9 percent over 10 years instead of 20, the EMI rises to about 12,700 rupees, but total interest falls to around 5.2 lakh rupees.

Choosing a tenure

A buyer can afford 13,000 rupees a month. Instead of choosing the longest tenure to get the smallest EMI, she picks a 10-year loan with an EMI just under her limit. She pays less than half the interest she would have paid over 20 years.

Thinking a lower EMI means a cheaper loan

A longer tenure lowers the EMI but greatly increases total interest. Always check the total amount you will repay.

Key takeaways

An EMI combines interest on the outstanding balance and principal repayment.
A 10 lakh loan at 9 percent for 20 years has an EMI of about 8,997 rupees.
Early EMIs are mostly interest; later ones mostly principal.
Longer tenures lower EMIs but raise total interest sharply.