The Power of Compound Returns

The Power of Compound Returns

The Power of Compound Returns

Compound returns or compounding is probably one of the most powerful concepts in the world of 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 people who understand compound interest can earn it, while the ones who do not end up paying it.

There are basically three variables or inputs to calculate compound interest: (1) starting principal, (2) expected rate of return and (3) length or period.

Despite being praised by mathematicians and the financial community at large, interest on loans was largely shunned by many of the world’s cultures and religions. Referred to as usury, which is the act of lending at interest or excessive interest was frowned upon and considered an act of enslaving one's brethren.

Compound interest was able to push through the historical negative connotation and today is a large part of our financial institutions from banking to investing.

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.

Simple Interest

So what is simple interest?

Simple interest is a percentage 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 thus increasing your capital over time.

For example, if you invested $1,000 into a one year fixed deposit with an annual interest rate of 5%. At the end of the one year, you would have $1,050, where $50 is the interest earned.


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 $1,000 at 5% annual interest rate. Therefore, at the end of the first year you make $50 on your investment. Now you re-invest the $1,000 principal and by year end make another $50.

Therefore, with simple interest, you make a total profit of $100 over two years.

Compound Interest

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 in interest. But instead of withdrawing this interest, you reinvest it for the second year along with your initial investment of $1000.

So for the second year, you have invested $1,050. Now, at 5% annual interest rate, your investment would be $1102.5. Here $1,000 was your initial investment and your profits are $102.50.

When you compare the simple interest and compound interest, you can see that with compounding you made an additional $2.50.

Simple Interest vs Compound Interest

Simple Interest vs Compound Interest

The above picture depicts the difference between simple and 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.

By compounding at the same 10% interest, you can see that by year 3, compound interest earned $12.10 - 21% more than the fixed 10$ return.

What is Compounding Returns?

Compounding is simply a process of making more returns on an investment by re-investing the earnings.

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

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.

Annual Compound Interest

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 $1,000 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 = $1,000

r = 5% or 5/100 = 0.05

n = 1

t = 5


$1,000 (1 + 0.05/1)^(1 * 5)

$1,000 (1.05)^5

Compounded Interest = $1,000 x 1.276281 = $1,276.28

This value of $1,276.28 can also be reached via the simpler formula where the interest is compounded once per period only.

CAGR

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:

CAGR Formula

CAGR Formula

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 $1,000; Final value of investment was $1,276.28; period of 5 years

Therefore, CAGR would be [($1,276.28/$1,000)^(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 Returns

Compound interest examples with two variations

Compound interest examples with two variations

The left side of the table shows an initial investment of $1,000 that gives a 1% annual return. The interest from the first year's investment is reinvested back into the second year and so on.

The right side of the table depicts the example when an investor adds $1,000 every year.

Two key points from the above table: time and the amount of money invested 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, interest rates set by the central bank become the benchmark for just about anything - from investments to debt.

Compounding can play a big role in certain types of investments where the investor receive regular payouts such as dividends or interest on bonds.

As a rough comparison, if you invested $10,000 in a dividend paying stock with an average annual return of 12% you would have $96,462 at the end of 20 years.

dividend investing vs non-dividend investing

dividend investing vs non-dividend investing

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 Compound Returns?

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

For investors holding bonds, the annual or bi-annual interest payments can be reinvested in purchasing other bonds or other securities. There are also specific bonds such as the zero coupon bonds which automatically include compounded returns.

The trade off is you do not get the interest payments but receive the face value of the bond and compounded interest at maturity.

In Summary

As shown in this article, compound interest is something that investors and consumers need to thoroughly understand.

When one understands the true power of compounding returns it can help investors make the right investment decisions with an eye on increasing their returns significantly with 'time' on their side.

Building upon this idea, the key aspect of successful compounding investing is time.

Compounding is extremely powerful when an investor starts young.

The key to compounding is of course saving and reinvesting the profits. 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, unless you ramp up the amount of additional money added each year.

Al Hill Administrator
Co-Founder Tradingsim
Al Hill is one of the co-founders of Tradingsim. He has over 18 years of day trading experience in both the U.S. and Nikkei markets. On a daily basis Al applies his deep skills in systems integration and design strategy to develop features to help retail traders become profitable. When Al is not working on Tradingsim, he can be found spending time with family and friends.
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