# The Fundamental of Finance: Time Value of Money

By: Tanmay S., Finance, Investing and Accounting Tutor, Chartered Accountant

Before you delve into this #rathersimplebutmadecomplicatedbythebigguys finance world, I would want to introduce you to one of the very basic and quintessential principles. For example, how your parents would have bugged you multiple times – just clear this particular exam and your life is all set then.

Ditto. Just understand this principle, and you have learnt Finance. Who am I kidding? But still, get a hold of this principle and you are already better than a lot of others.

## What is the Time Value of Money?

The value of money received today is more than the value of the same amount of money received at a future date (take your time, read it again).

Suppose you have earned a cash bonus for being the student of the year. You have an option — either to take \$ 1,000 today or wait for a year to complete your Master’s in Finance and receive the amount in 1 year from now.

Now, what should you do?

You go to your bank and ask them what interest you would earn for 1 year on \$ 1,000. And the bank offers you a 10% interest rate. So, now if you collect the cash bonus today and invest it with the bank, you shall have \$1000 + 10% Interest on \$1000 (i.e. \$100) =\$1100 by the end of 1 year.

Isn’t that better than receiving \$1000 after you complete your Masters?

Well, to be fair, it isn’t rocket science and you don’t have to be Elon Musk to understand this. But the real trick is how to apply this simple principle.

## Key Concepts

To begin with, let us just assign some random names to these simple concepts we covered in our example above. (remember the big guys, we talked about in our hashtag, yep! They create these random names)

Present Value of Money (PV) – In our example, the bonus amount received today, \$ 1,000, would be our Present Value. Present Value is the money’s worth today, i.e. in Year 0 (Y0).

Future Value of Money (FV) – \$ 1,100 received from your bank in 1 year from now (Y1) would be Future Value. It is the amount of money the bank will return to you on the maturity of your deposit. Future Value is the money’s worth in the Future.

Future Value = Present Value + Interest Earned in Y1

Rate of Interest (i) – 10% in our example is the interest you would earn on your deposit.

Time Period (n) – 1 year is the time period in our example.

## What is Compounding?

Now, let us talk about Compounding.

Well, there’s nothing more to stress the importance of Compounding.

But what is compounding? Compounding is what makes your wealth grow ‘exponentially’. Literally. Everyone who has been pestering you to start saving early knows the value of compounding. The earlier you save, the more time your money gets to grow. Compounding is ‘earning interest on your interest’

Coming back to our example. Suppose after your Master’s in Finance, you get an excellent job and you decide not to withdraw the reward money from your deposit. And you keep earning 3% interest per year.

In the first year, you earn interest on the original bonus of \$1000 (also known as Principal)

Interest in Year 1 = 10% of \$1000 = \$100

Now, in the second year, this interest of \$100 gets accumulated in the original amount, increasing your Principal Amount. Therefore,

Interest in Year 2 = 10% of (\$1000 + \$100) = 10% of \$1100 = \$110

Interest in Year 3 = 10% of (\$1100 + \$110) = 10% of \$1210 = \$121

And so on.

So basically, you are not earning 10% on your original bonus amount of \$1000 every year. Had that been the case (Simple Interest), you would have earned an interest of \$100 every year, but as the more number of years you stay invested, the interest amount keeps on increasing and your wealth keeps on compounding. Have a look at the difference between the Wealth amount at the end-of-year 15. The \$1000 bonus if compounded at 10% for 15 years gets you back \$4177 whereas a simple interest of \$100 each year gives you just a bit more than half of what you can get by compounding.

Oh, didn’t I use the word exponentially before? Compounding helps you grow your wealth exponentially

To arrive at the value after 15 years, you will have to exponentially raise the interest rate to 15.

Value at the end of 15th year = \$ 1,000 X (1 + 10%)15 = \$4,177.25

Connecting it back to our Present Value & Future Value, here is a rather simple formula!