# The Power of Compound Returns

Compound returns or compounding is probably one of the most powerful concepts in the world of financial investing. Compounding is often dubbed as the eighth wonder of the world, at least as far as the investment world is concerned.

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Compound interest as it is called mathematically is deceptively simple, to the point that Albert Einstein called it the greatest discovery of all time in mathematics. Einstein further went on to say that the people who understand compound interest can earn it, while the ones who do not understand end up paying it.

There are basically three variables or inputs that one needs to be concerned with when it comes to compounding and these three variables are of course the most important when it comes to determining your returns.

Despite being praised by mathematicians and the financial community at large, interest on loans was largely shunned by many of the world’s largest cultures and religions. Referred to as usury, which is the act of lending at interest or excessive interest; the concept of interest (and thus by definition simple and compound interest) managed to survive the age of time.

Today, compound interest and financial investments go hand in hand and is often used as the one of the most widely used metrics in the world of investing. While compounding can clearly magnify the returns on an investment, it can also equally magnify the liabilities when you take out a loan that is based on the compound interest.

## Understanding simple and compound interest

When talking about compound interest, it is always best to understand simple interest in order to truly realize the power of compounding.

So what is simple interest?

Simple interest is where you get a percentage (or the interest) on your investment paid to you after a fixed period of time, usually one year.

Compound interest on the other hand reinvests the interest received at the end of every year or a certain period and increases your capital which in turn increases the interest you earn the following year.

For example, if you invested $1000 into a one year fixed deposit with an annual interest rate of 5%. At the end of the one year, you would have $1050, where $50 is the interest earned.

This $50 is nothing but 5% of the investment of $1000 that you made. This is simple interest at work.

Now, if you had the same option as above, but opted for a 2 year fixed deposit term, let's see two ways you can make money.

In the first option, you invest $1000 at 5% annual interest rate. Therefore, at the end of the first year you make $50 on your investment. Now you invest back the capital of $1000 and by the end of second year, you again make $50.

Therefore, with simple interest, you make a total profit of $100 in the two year period.

Taking the same example, let's see how returns are different when you opt for compound interest.

At the end of the first year, you make $50 interest. But instead of withdrawing this interest, you reinvest it back for the second year along with your initial investment of $1000.

So for the second year, you have invested $1050. Now, at 5% annual interest rate, your investment would be $1102.5. Here $1000 was your initial investment and your profits were $102.5.

When you compare the simple interest and the compound interest, you can see that with compounding you made an additional $2.50. As the number of years grows at the same annual interest rate, but with compounded returns, you can expect your returns to also increase significantly as compared to simple interest.

The above picture gives a visual explanation between the simple interest and the compound interest. The above example shows that while the interest rate of 10% was applied to both, with simple interest, the $10 interest was paid every year.

On the other hand, with compound interest, the interest from the previous year is added back to the capital, thus increasing the interest for the next year. By compounding at the same 10% interest, you can see that by year 3, compound interest had an interest if $12.10 instead of $10 when the investment started.

## What is compounding?

Compounding is simply a process of making more returns on an investment by re-investing the earnings on the investment. In other words, compound interest is when the interest that is accrued beings to accrue interest on itself.

It might seem complicated to understand but very simple in concept. For compound interest to work, there three things required, which are the reinvestment of the earnings and the period of time and the third variable which is the rate of return.

Compound interest helps investors or savers to grow their investments exponentially and is particularly advantageous to young investors as time is the greatest variable that works in their favor.

Mathematically, compound interest or the compounded return is the rate of return expressed as a percentage. The compound interest reflects the cumulative effect a series of profits or losses have on the original investment amount over a period of time.

The compound interest, which is reported as a percentage refers to the annualized rate of return at which the invested capital has compounded over the period of time.

The formula for annual compound interest is as follows:

Annual compound interest = the future value of the investment including interest

P = Principal amount (initial deposit or initial investment)

r = annual interest rate in decimal (ex: 5% annual interest rate will be expressed as 5/100 or 0.05)

n = the number of times the interest is compounded every year

t = the number of years or duration of the investment

A simpler version of the above formula is also read as:

In this example the interest is compounded once per period.

For example, if you had an amount of $1000 in a fixed deposit account that has an annual interest rate of 5% compounded yearly, then the value of the investment after a period of 5 years would be calculated as:

P = 1000

r = 5% or 5/100 = 0.05

n = 1

t = 5

1000 (1 + 0.05/1)^(1 * 5)

1000 (1.05)^5

1000 x 1.276281 = 1276.28

This value of $1276.28 can also be reached via the simpler formula where the interest is compounded once per period only.

Compound interest, when expressed in annualized terms is referred as the Compound Annual Growth Rate or CAGR for short.

The CAGR represents the annual growth rate of the investment over a period of time. CAGR is derived by dividing the value of the investment at the end of the period by the value of the investment at the start.

The result is raised to the power of one divided by the period of time and the resulting amount is subtracted by one.

Mathematically, CAGR is calculated as:

Fi = Final value of investment

Oi = Original value of investment

t = period of time

If we go back to the example from the previous section, we can calculate the CAGR.

Original value of investment was $1000; Final value of investment was $1276.28; Period was 5 years

Therefore, CAGR would be [(1276.28/1000)^(1/5)] -1

= [1.27628^0.2] – 1

= 1.05 – 1

= 0.05 or 5%

Therefore, the compounded annual growth rate or CAGR for the investment over the 5 year period is 5%.

## Understanding the power of compounding

The best way to understand the power of compounding is by means of an example shown below.

The left side of the table shows an initial investment of $1000 made into a fund that gives a 1% annual return. The interest from the first year's investment is reinvested back into the second year and so on.

As you can see in the above table over a period of time, the interest accrued in the earlier years also starts to contribute to the capital thus exponentially increasing the returns by the end of the 5-year term.

On the right side of the table, the same example is shown but with the investor adding an steady $1000 every year. Taking the compounding factor into question, this time the returns generated are even higher.

What the above table illustrates is two key points, which is time and the amount of investment that is made, which when compounded can greatly increase the returns.

## What are the benefits of compounding in finance and investing?

Interest rates play a major role for any type of investing. After all, the interest rates set the central bank become the benchmark for just about anything, from investments to debt. Therefore, it is safe to assume that interest rates are central to investing.

The accumulation of investing is a major concern, both for lenders and investors at the same time. Interest can play a dual role as it can be beneficial to one's investment but at the same time it can also end up eating into one's investments.

Compounding can play a big role in certain types of investments where the investor gets regular payouts such as dividends or interest on bonds that are held. When done correctly, such type of investments through the power of compounding can help investors to quickly scale up their investments.

As a rough comparison, if you invested $10,000 in a dividend paying stock with an average annual return of 12% which includes both the appreciation of the stock price and the dividend payments, the result would be $96,462 at the end of 20 years.

On the same note, if you invested $10,000 in a non-dividend paying stock with the same annual return, it would have given a total return of $56,044, close to half of the amount one would have earned if they had invested in a dividend paying stock.

The above chart compares both the values. As you can see, the power of compounding clearly stands out in certain cases of investments.

## What investments are best for utilizing compounded returns?

Besides dividends, a classic case of compounding the returns is applicable with bank deposits such as on savings accounts or fixed term deposit accounts and as well as certificates of deposits.

For investors who are holding bonds, the annual or bi-annual interest payments can be reinvested in purchasing other bonds or reinvesting the money into other forms of investments. There are also some specific types of bonds such as the zero coupon bonds which automatically include compounded returns.

Here, the only trade off is that you do not get the interest payments but you receive the face value of the bond and additionally the compounded interest at maturity.

Even for regular stock investors who do not necessarily focus on dividend paying stocks, the annual rate of return can be used to calculate how one can compound their profits over a period of time.

As shown in this article, compound interest is something that investors need to take time to thoroughly understand as it helps not just from an investing point of view but also helps to understand when one is taking out any loan, be it a short term personal loan or a mortgage loan.

When one understands the true power of compounding it can help investors to pick the right investing instruments and also have a firm plan through which they can expect to increase their returns significantly over a period of time.

However, as with most things, one of the key aspects to successful investing with compounding is the time itself. Compounding can be very powerful when an investor starts young as it can help them to build a significant amount of returns by the time one reaches retirement or a certain goal in life.

The key to compounding is of course saving and reinvesting the profits made from the investment in question. Thus, for those investors who have started investing at a later stage, it would be difficult to truly take advantage of the power of compounding.