Appreciating the effects of compound returns is one of the basic building blocks of becoming a great investor. Our ability to create wealth over a lifetime is the direct result of the amazing power of compound interest. For instance if we were to put $1000 in an account for a child born today, and that person lived a normal lifespan of around 80 years, while earning a 10% return, that simple $1,000 would grow to over $2,000,000.

Compound interest is an incredible concept to have working on your side. Albert Einstein is even said to have called compound interest the 8th wonder of the world. As investors we should try to understand compound returns to make sure we are doing everything we can to enjoy its benefits. If we are able to develop the correct tools as investors to achieve strong returns and have the willpower to stick with it over the long term, the mathematics of compounding take care of the rest.

A Penny Doubled Every Day

In order to demonstrate the effects of compounding allow me to give you a proposition. You can have either one of two options: would you rather have 1) $100,000 or 2) the amount equal to a penny doubled every day for month?

Maybe $100,000 isn’t interesting enough.

How about $1,000,000 or a penny doubled every day for a month? How about $5,000,000? How much would it take?

My guess is by now almost everyone would have taken the sure money. Because how much could the penny really grow to in only a month? It’s only a stupid penny after all.

The truth is that even at $5,000,000 you would have shortchanged yourself by taking the sure money rather than the penny.

A penny doubled every day for 31 days is actually equal to $10,700,000. That is pretty remarkable given that we started with just a penny.

That is the power of compounding: a simply penny can turn into a huge sum given the right circumstances. As our money grows, each additional time period produces greater and greater wealth.

It’s like a snowball rolling down hill. At first it starts small and is rather unimpressive. But as it continues to grow and pick up speed it begins to take on a life of its own. The size of the snowball begins to grow exponentially with each additional turn until at some point each turn is adding so much snow you wouldn’t even recognize it as the small thing you started with. The compounding of money works the exact same way. Even when starting with only a penny, just like a snowball, by the time we have reached the 31^st turn on our money we are adding a tremendous amount of wealth.

The Man Who Invented Chess

There is a parable told about the man who invented chess. It is said that the king so enjoyed this new game he summoned the inventor to the castle so he could personally thank him.

When the inventor came before him the king exclaimed, “For this amazing invention you deserve a great reward. Name anything in the kingdom and it will be yours.”

The man thought for a moment and then stated, “All I request is that you take a grain of rice and place it on the first square of the board. Then take two grains and place it on the second square. Four grains of rice on the third square, eight on the fourth, and so forth. When you have placed the right amount of rice on the board, that will be my reward.”

The king was actually offended by this meager request. “I offer you anything in the world, and all you ask for is some rice. Perhaps you are not that smart after all.”

The king dismissively motioned for his attendants to see to it that the man received his rice so the fool could be sent on his way.

However, after a short while the attendants had not yet returned with the man’s rice. The king began getting irritated wondering what could possibly be the hold up.

Soon the king’s treasurer nervously appeared with some unfortunate news. “Your highness I have been working hard on getting this man his rice. Unfortunately there is a problem. I have done the calculation and the amount of rice the man asks for, well we don’t have that much at the castle.”

“Impossible,” the king shouted. “I am the richest man this kingdom has ever seen.”

The treasurer went even further. “Your highness not only do we not have that much rice in the castle, we do not have that much rice in all of our lands. And not only do we not have that much rice in our kingdom, that amount of rice has never existed.”

The king could not believe that in his simple request, the man who had asked for all of the wealth of the world. The man’s request amounts to approximately 461,000,000,000 metric tons. If we fast forward to today, at current rice prices, the amount of rice the man requested would amount to $300 trillion. This is about the entire wealth of the planet. The effects of compounding are pretty incredible.

The Rule of 72

There is a simple rule of thumb to help calculate how long it will take you to double your money given a certain rate of return. It revolves around the number 72. All you have to do is take 72 and divide it by the annualized rate of return you are aiming to achieve. The result is the number of years it will take to double your money.

# Of Years to Double Money = 72 ÷ Rate of Return

For instance, if you were aiming to achieve a 5% rate of return you could calculate how long it would take to double your money. Simply take 72 ÷ 5 = 14.4 years. You will double your money approximately every 14 years if you achieve a 5% rate of return over your lifetime.

You could also reverse the process to figure out what rate of return you would have to achieve in order to double your money in some specific time frame. For example, let’s say you set as a goal to double your money every decade of your life. What rate of return would you have to achieve? Take 72 ÷ 10 = 7.2%. If you can get a 7.2% rate of return you will double your money every 10 years.

 

Important Lessons of Compounding

1. The Hockey Stick Effect: When you first start compounding the results may not seem all that impressive. In the beginning the results may be so small as to be almost imperceptible. But as time goes by the effects of compounding begin building steam to the point where there is an inflection point. The graph of exponential growth looks like a hockey stick. Our job is to have the patience and determination to get past the initial stages where it may seem like not much is happening.

2. The Investment Period is Important: Start Early. Let’s say you wanted to retire at age 65, but didn’t start saving until late in life such as age 55. In those 10 years, at a typical equity rate of return of 8%, your 100K would turn into 215K. Not bad, but compare it to the amount of wealth you could have if you would have started earlier. If that same person earning 8% would have started at age 35, their 100K would have grown to $1 million. That is a huge difference.

3. The Amount You Are Able To Invest Helps A Lot: You have to invest money to make money. The more, the better.

Our wealth can grow over time when starting with a lump sum, but adding additional funds as we go along helps as well. The machine of compounding is fueled by the principal you are working with. The more funds you feed the machine the better. Compare the amount received over 30 years at 8% with and without an additional 10K every year. Without the additional contribution we have $1 million, but with an extra 10K we end up with $2.1 million. That’s double the money by only adding 1/10 of our original investment each year.

4. Rate of Return Matters a Lot: Compare the sum over 30 years from achieving a 5% return vs. a 15% return.

It would be easy to think that because you received 3X the return you would end up with 3X the money. This would be wrong. Because of the effects of compounding, an investor who gets 15% vs. 5% will not have 3X the money but rather 15X the money. Rate of return matters a lot, especially over long time periods.

Conclusion

The math of compounding will take care of its self as long as we set it into motion and have the discipline to stick with it over the long term.  The lessons from studying compound interest reinforce my belief in the power of value investing. They work hand in hand and feed off each other.  Value investing allows us to take full advantage of compounding by rationally allocating capital for the long term. Value investing offers a simple way to compound wealth: seek out businesses that have durable competitive advantages that allow them to earn high returns on invested capital, but only purchase these businesses when we can do so at a large discount. We want to buy things for less than they are worth. By buying high quality businesses for substantially less than they are worth and holding for the long term we are taking full advantage of the lessons learned from compound interest.