EMI Calculation Formula With a Worked Example

The EMI formula

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

P = loan amount
r = yearly interest rate / 12 / 100  (the monthly rate as a fraction)
n = number of monthly instalments

This is the reducing-balance method that Indian banks use for home, car, personal and education loans. Interest is charged each month only on the amount you still owe, not on the original loan.

Worked example: ₹10 lakh at 8.5% for 20 years

1. P = 10,00,000.
2. r = 8.5 / 12 / 100 = 0.0070833 a month.
3. n = 20 x 12 = 240 months.
4. Put them into the formula: the EMI comes to ₹8,678 a month.
5. Total paid = 8,678 x 240, about ₹20,82,776. Take away the loan of ₹10,00,000 and the interest is ₹10,82,776.

So over 20 years you pay back a little more than twice what you borrowed. The calculator shows the exact EMI with paise; the figures here are rounded to the rupee.

Why the early EMIs are mostly interest

In the first month you owe the full ₹10 lakh, so the interest is 10,00,000 x 0.0070833 = ₹7,083. Only the remaining ₹1,595 of the EMI brings the loan down. Next month the balance is a little lower, so the interest is a little lower and a little more goes to principal. This repeats until the loan is closed.

In the first five years you pay about ₹4,01,966 of interest and only ₹1,18,728 of principal. After 10 years, half the tenure, about ₹7 lakh of the ₹10 lakh is still owed. The year-by-year schedule in the calculator shows this for your own loan.

How the tenure changes the total interest

Going from 20 to 30 years lowers the EMI by under ₹1,000 a month but adds almost ₹7 lakh of interest. Going from 20 to 15 years raises the EMI by about ₹1,170 and saves about ₹3.1 lakh.

How the rate changes it

One percentage point on a 20-year loan of ₹10 lakh moves the total interest by about ₹1.5 lakh. It is worth comparing banks before you sign.

The idea behind a prepayment

A prepayment goes straight to the principal, so every later month is charged interest on a smaller balance. It helps most in the early years, when the balance is highest. The calculator does not model prepayments, but you can see the effect with it:

1. Open the schedule and note the balance left at the end of a year. In our example it is ₹8,81,272 after 5 years.
2. Enter that balance as a new loan with the same rate and the years left (15). The EMI is ₹8,678 and the interest still to pay is about ₹6,80,810.
3. Now take away your prepayment. With ₹1 lakh paid, enter ₹7,81,272 for 15 years. The EMI drops to ₹7,693 and the interest left is about ₹6,03,557.

That ₹1 lakh saves about ₹77,000 of interest if the bank lowers your EMI. If instead you keep paying the same EMI and the bank shortens the tenure, the saving is usually bigger. Ask your bank which option it offers and whether it charges a fee for prepayment.

If your bank gives the rate per month, multiply it by 12 before you enter it. 0.75% a month is 9% a year.

Why your bank's EMI can differ

• Banks round the EMI and may count interest from the disbursal date, so the first EMI can be different. A gap of a few rupees is normal.
• Floating rates change over time. The calculator holds the rate you enter for the whole loan.
• Processing fees, insurance and GST on charges are not part of the EMI shown.

Common questions

What is the EMI on a ₹50 lakh home loan at 8.5% for 20 years? ₹43,391 a month.

What is the EMI on a ₹5 lakh personal loan at 10.5% for 5 years? ₹10,747 a month, with ₹1,44,817 of interest in total.

What if the rate is 0%? Then the EMI is simply the loan divided by the months: ₹10 lakh over 120 months is ₹8,333 a month.