Updated on: June 13, 2020 ; Wealth & Value
What is compounding?
Compounding is the silent wonder of investing. The magic of this starts to reveal itself only after a long period of time, and the impact grows exponentially with time. It is a simple concept where your seed investment grows at a certain rate. In addition to that, the growth earned (interest) on the investment also grows at the same rate.
Let’s take an example to explain it in a better way. Assume you have made an investment of 100 rupees. You invested it in an instrument with a 10% growth rate per annum. One year later, you earn the growth of 10 rupees on your initial investment. We will call this growth as interest. The initial investment is called the principal. So the value of your investment after one year becomes
100 (pricipal) + 10 (interest) = 110
What happens if you stay invested for another year? The same growth rate applies to the initial investment as well as the interest earned. So the growth earned in the second year is 10% of 100 (initial investment) + 10% of 10 (interest).
10 + 1 = 11
Thus, at the end of 2 years your investment grows to =100 + 10 + 11 = 121.
The interest earned also gets re-invested in the same instrument and gets treated as additional principal. These additional gains from the re-invested interest keep getting added every year, till the period you stay invested. This phenomenon of added growth on the capital invested and the interest earned is known as compounding.
What is the math behind compounding?
Now that we have covered the concept, using a very simple example. Let’s look at how to compute the compounding effect over a longer time frame. Don’t worry, the logic behind it is very straight forward, and I will do my best to explain it in very easy terms. We will elaborate on the example we used earlier.
The principal (seed investment) of 100 rupees with a growth rate of 10% per annum, after one year becomes:
= 100 (principal) + 10% of 100 (interest)
= 100 + 10
= 110
This can be written as :
principal + growth rate x principal
principal x (1 + growth rate)
The following year, this increased value of the investment becomes the starting investment amount. Let’s call it principal2. We can write it as:
principal2 = principal x (1 + growth rate)
So, applying the same logic the value of the investment after two years becomes:
principal2 x (1 + growth rate)
principal x (1 + growth rate) x (1 + growth rate)
principal x (1 + growth rate)2
Extending this logic to n years we get the formula for compounding as:
principal x (1 + growth rate)n
See, it wasn’t that complicated! If this equation looking familiar to you, read the article on ‘time value of money‘.
So, let’s get a better hang of things by looking at a few illustrations.
Illustration 1:
We assume the following. principal = 1000 rupees; growth rate = 8% per annum. The table below gives the year-wise value of your investment at the end of each year, provided you stay invested for that many years. We have taken a time frame of 20 years here. You can stay invested for as long as you wish 😊.
What do you notice from the highlighted rows in table 1?
It takes almost 9 years to add the first 1000 rupees, which equivalent to the seed investment or principal.
The addition of next 1000 comes in the next 5 years.
The third 1000 is added in the next 3 years.
It takes 18 years to grow your initial investment by 4 times. But the time gap to add each thousand keeps on decreasing. This is the magic of compounding. You have to stay invested for long to experience it. Let’s look at another illustration.
Illustration 2:
We will make just a small adjustment to the illustration above. We will increase the growth rate by 1% and make it 9%. Let’s observe the impact of a 1% change in the growth rate.
Do you see what difference a 1% change in growth rate makes? If you compare the investment value of both the tables at the end of the first year, you will find just a small difference of 10 rupees.
But if you go down the table, you will notice the difference getting significant. The investment amount doubles in 8 years in the second case, versus 9 years in the first case. A difference of one whole year.
Similarly, the additions of subsequent 2 thousands also happen 2 years earlier.
At the end of 20 years, the second case would have earned you a whole 1000 rupees more than the first case, a difference of more than 20%. Isn’t that amazing? Just a small difference of 1% in growth rate results in 20% more value at the end of 20 years.
Real-world examples of compounding
It is time we look at some real-world examples of compounding. We will take examples of two different types of investments. These will help you understand how the effect of compounding works differently for varied scenarios. To understand the basics of investments, please click here.
In the first scenario, we will look at fixed deposits. They give fixed and assured returns as they are guaranteed by banks. They are one of the safest investments available, although they have a relatively lower rate of return (growth rate).
Assumption: The principal invested is 10,000 rupees at a fixed rate of 7% per annum. The following graph depicts the yearly value of the investment for the next 20 years. Please note, there are no fixed deposits for 20 years in the real world. But for the sake of our understanding, we will assume that one exists.
You can notice that the investment grows at a steady rate. It follows an exponential trend. The returns are almost guaranteed in fixed deposits. The value at the end of 20 years is around 38,700 rupees, an appreciation of 3.9 times.
The next scenario is where we look at the price movement of equity stock. Let’s look at ‘reliance industries’ and track its price movement from 2000 till 2020. Assume you bought just one share of reliance on 6th June 2000. The graph below shows the price of a single share of reliance industries and its price movement from 2000 till 2020.
It will be difficult for you to read the values as the scale is very large. So, I will help you with the numbers here. On 6th June 2000, a single share of reliance was available at 83.9 rupees. This is after adjustments for all the bonuses and stock splits. 20 years later, the same share was priced 1,541.61 on 3rd June 2020.
This is a growth of more than 18 times in a span of 20 years. The compound annual growth comes out to be 15.66%, also known as CAGR.
Can you see the stark difference in the returns of these two types of investments? Also, notice that in graph 2, the trend in growth is nowhere close to the steady pattern you notice in graph 1.
Another critical observation is that there was a long period between 2009 and 2017, where we see no movement in the price. In fact, there were many occasions where the price dipped. So, there are higher chances that you might lose money if you choose the wrong investment vehicle and do not stay invested for long. Because unlike fixed deposits, there are no fixed patterns in stock price movements.
By now, if I have done justice to your time, you would have understood how compounding works and how it works differently for various instruments.
What does it mean for you?
You will have to stay invested for a long time period to experience the true benefits of compounding. The time required to add the equivalent amount as your principal investment goes down drastically as your investment time horizon increases.
As the growth rates differ from one type to another, you will have to be very careful while choosing the right investment vehicle. Understand the risks associated with your investments. Also, note that returns for all investments are not equally steady and predictable.
Choose wisely and stay invested for long. There are no short cuts for this.