What is the way we can generate compounding investment returns? To do this we will have to understanding the power of compounding first.

Before one starts to invest money, it is important to appreciate the power of compounding.

It is the power of compounding that can generates larger cumulative returns over a period of time.

In long term investing, the power of compounding plays a major role. A compounding investment returns makes once investment corpus grow at a very fast rate.

What makes the power of compounding so important for long term investors?

The power of compounding is a theory which helps the invested money to multiply geometrically if held for a long term.

The speed at which the money multiplies depends on two factors: first is the rate of return and, second is the holding period.

A combination of investment returns and holding periods gives varied results like exemplified below:

Low returns and low holding periods will multiply the invested fund slowly.

Hi returns and high investment returns will multiply the invested fund faster.

This is obvious.

But to understand the real power of compounding we can take any combination of return and holding time to see the impact of compounding returns.

From the above chart a pattern is very evident. “The speed of compounding of investment returns become faster in later years”.

The chart clearly shows that it has taken the invested money ($1,000) **13 years** to grow to $10,699 @ 20% per annum. But it grows to a whopping $55,206 in next just 9 years.

Another observation is easy to conclude. The speed of compounding of investment returns are faster when the rate of returns are higher.

Seeing the pattern of the curves in the above chart, after the 13th year, the money growing @ 20% shows faster growth than money growing @ 18%.

This observation also lead the experts to derive a very convenient investment rule that will help us to understand the power of compounding even more clearly. This is called the rule of 72.

## Compounding investment returns and the rule of 72

Rule says that the money doubles when the product of the rate of return and time horizon is equal to 72.

So what does this rule tells us about the compounding investment returns?

Let’s understand this with an example.

It will take 9 years for the investment to double itself if the rate of return is 8%.

8 X 9 = 72

It will take 12 years for the investment to double itself if the rate of return is 6%

12 X 6 = 72

Suppose your investment got doubled in a period of 4 years. What is the annualized rate of return you earned? It is 18% per annum.

18 X 4 = 72

## Compounding investment returns and time value of money

Now we know what a power of compounding can do to our invested money. At the rate of 15% per annum, our invested money will double every 4.8 years.

It means, if you invested Rs. 1 Lakh today yielding 15% return, after 29 years the same money with inflate and become Rs.64 lakhs.

This is the what is the real power of compounding.

But aren’t we suppose to talk also about time value of money?

Yes, sure.

If the money is invested @ 15% CAGR, after 29 years it becomes Rs. 64 lakhs.

But what happens if the money was not invested?

The answer is simple, either the money gets spent or it continues to be Rs.1 lakhs even after 29 years.

This requirement to grow money by putting it into suitable investment option is not only a wilful desire, it is a necessity as well.

Remember, investment is a necessity, it is not an option.

It is absolutely necessary that money keeps yielding compounding investment returns over and over again.

Why?

There is a theory which says:

“A dollar of today is worth more than a dollar of tomorrow”.

In other words, the money becomes weaker with passing years.

Why it is so?

To understand this, lets take another example.

#### Example of two millionaires…

Suppose there are two friends, Jack and Sam. Both of them are 25 years of age and has $10 million dollar in their bank account.

The money in bank for both of them is so huge that they need not bother about investing, right?

Sure, at least this is the way majority people will think if they have $10 million in kitty.

People who does not know the necessity of investing money do become complacent with their income/savings. But this is a big mistake.

Lets see how.

As investment was not a priority for Jack and Sam, Jack decided to park his $5 million in a debt linked mutual fund for next 10 years. Balance $5 million he kept with himself to maintain his standard of living.

But Sam decided to continue a care free and lavish lifestyle. He kept with himself the full $10 million to support his standard of living.

So what change these two different approach to investing will bring to Jack’s and Sam’s lifestyle?

At the end of 10th year, Jack spent his $5 million but he also had another Rs.10 million dollar in his investment portfolio. His invested $5 million became $10 million @ 8% per annum in 10 years.

During the same period, Sam also exhausted $5 million dollar. But as Sam did not invest, what remained with him was only $5 million.

So what Jack and Sam had with them after 10 years?

Jack has $10 million, and Sam has $5 million.

Now, as Sam’s net worth is half of Jack. What Jack can do in next 10 years, Sam cannot do the same.

It means, for the next years, Sam will not be able to afford the same lifestyle as that of Jack.

Till today, both of them has spent $5 million on themselves. Jack can afford to do the same for next 10 years again. But for Sam, he cannot afford to spend as lavishly as Jack.

So what does this mean?

By not investing his money, Sam has actually harmed his power of spending. This is why it is said that, investing money is a necessity, it is not an option.

##### Time value of money

Due to compounding of the invested money $1 of today will become $1.05 after 1 year, if ROI is 5%.

The invested money $1 of today will become $1.16 after 1 year, if ROI is 16%.

While our investments makes our money grow with time, there is something else around us which makes our money shrink with time.

It makes out money weaker with every passing year.

I am talking about inflation.

Suppose inflation rate ifs 5.9% per annum. It means $1 of tomorrow (1 year from now) will be equivalent to $0.945 of today.

Means, if 1 Kg of apple costs $0.945 today, the same apple will cost $1 after one year @ 5.9% inflation.

It is the compounding investment returns that come as our savior from the wrath of inflation.

A suitably invested money will grow at a fast rate so as to beat the negative effects of inflation.

## Compounding of money and Compound Interest Formula

How to calculate the ‘future value’ or ‘present value’ of money by a mathematical formula?

Most of us have learnt the Compound Interest as part of our mathematics curriculum in school. They same formula can be used to calculate the present value and future value of our money.

This formula can be used to calculate future and present value of our investments.

Suppose one invests $1,000 for 7 years @ 15% per annum. What will be the appreciated value (FV) after 7 years?

FV = $1000 x (1+15%)^7 = $2,260.

This formula can also be used to calculate present value of future cash flows.

The concept of present value is often used in value investing to estimate intrinsic value of companies.

To understand how we can use the concept of present value, lets take an oversimplified hypothetical example.

##### Example 1:

Suppose you are approached by your LIC agent who wants to sell you an ULIP. This plan will cost you $1,000 today. But it promises you to pay back your $1,000 back after 10 years with an additional bonus of $1,100.

How you can decide if this is good investment or not?

You can use the compound interest formula to draw your conclusion.

**PV = FV / (1+R)^t**

FV = $1000+$1,100 = $2,100

R = Discounted Rate (Risk Free Rate) = 7.5% per annum

t = 10 years

PV = 2100 / (1+7.5%)^10 = $1,019.

Means, in today’s terms, the endowment policy is adding an additional $19 to your pocket.

This return is modest (>7.5% p.a.). The return are not very high but at least it is not eating away your money (inflation).

##### Example 2:

Suppose you are approached by a broker who wants to sell you a residential property during its project launch stage. This property will cost you $100,000 today. But it has potential to give your back $140,000 in next 4 years.

How you can decide if this is good investment or not?

Again, you can use the above compound interest formula.

**PV = FV / (1+R)^t**

FV = $140,000

R = Discounted Rate (Risk Free Rate) = 7.5% per annum

t = 4 years

PV = 140,000 / (1+7.5%)^4 = $104,832.

Means, in today’s terms, this investment is adding an additional $4,832 to your pocket.

This return is good.

This return is good (much more than 7.5% p.a.). The return is high. It beats inflation by a big margin.

## Examples of Compounding Investment Returns

##### #1. Equity based large cap mutual funds

Average returns in last 5 years: **18.24% p.a**.

Using rule of 72, this mutual fund doubles the money every **4 years**.

Value of $1,000 invested in such a large cap fund after 10 years will be **$ 5,300**.

##### #2. Equity based multi cap mutual funds

Average returns in last 5 years: **21.88% p.a**.

Using rule of 72, this mutual fund doubles the money every **3 years, 4 months years**.

Value of $1,000 invested in such a large cap fund after 10 years will be **$ 7,200**.

##### #3. Equity based mid cap mutual funds

Average returns in last 5 years: **27.81% p.a**.

Using rule of 72, this mutual fund doubles the money every **2 years, 8 months years**.

Value of $1,000 invested in such a large cap fund after 10 years will be **$ 11,600**.

##### #4. Equity based hybrid mutual funds

Average returns in last 5 years: **19.11% p.a**.

Using rule of 72, this mutual fund doubles the money every **3 years, 9 months years**.

Value of $1,000 invested in such a large cap fund after 10 years will be **$ 5,700**.

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