# The Mathematics behind EMI

This is continuation of Article : What is EMI and How it is calculated , which shows how to calculate EMI using a spreadsheet application like Excel.

This article talks about the Concept behind EMI. Actually, it may sound ridiculous, but the concept was taught to all of us in Primary or may be Secondary school. Well, I am talking about the concept behind Compound Interest. This is the same very concept that is used in EMI.

Now, I am sure, you may not remember the compound interest formula. Let me remind you. The formula goes like this.

**Amount = Principle * ( 1 + Rate of Interest
/100) ^ No. of years **(If the interest is compounded annually)

This same formula is also used for calculating the Future Value of an investment, or Present Value of a future return. What we know is, if we keep Rs. 100 in the bank for 1 year, we get Rs. 110/- if the bank is willing to give 10% interest p.a.

**This is the concept of Time value of
money. Rs. 100/- today is equal to Rs. 110/- after one year. Or conversly,
Rs. 110/- after one year is equal to Rs. 100/- today.**

Formula for calculating Future Value of Present
Investment is : **FV = PV * ( 1 + Rate of Interest /100) ^ Period**

Formula for calculating Present Value of a Future
return is : **PV = FV / ( 1 + Rate of Interest /100) ^ Period**

**Remember to divide the annual interest rate by
12 in case of monthly reducing balance**.

Now try this with your EMI.

Lets say you are paying 120 installments, for a Loan of Rs. 1,00,000/- at a rate of interest of 11% p.a. Your EMI will be Rs. 1377.50 for this amount.

Take a Excel sheet. In column A, Put nos. 1,2,3… 120. In the Column B, in front of each of the no. 1,2…120, put the EMI amount of Rs. 1377.50

Now discount each of the values. for example,

Present value of the First EMI will given by PV(1) = 1377.50 / ( 1 + 11%/12) ^1

Present value of the Second EMI will given by PV(2) = 1377.50 / ( 1 + 11%/12) ^2

Present value of the Third EMI will given by PV(3) = 1377.50 / ( 1 + 11%/12) ^3 and so on..

All that we have done is reduced all the future EMI’s to present value using the PV formula.

Now, if you add all these PV’s, you will get the Loan amount. So all that you are returning to the banks is what they gave you. And since you are returning in future, they are charging you the time value of money.

I hope I have been able to clarify the concept. If you are still confused, feel free to write to me at ktu@elearnindia.com and I will try again.. Please let me know your views.