Sunday, April 17, 2011

Confounding Compounding Chronicles

A big reason that I am a fiscal conservative is that I understand the power of compound interest.   If it is working for you, it makes your life easy.  If it is working against you, it will ultimately bury you.

Over the years I have enjoyed collecting stories showing the power of compound returns.  No matter how many times I see these stories they always seem to be confounding.  It just doesn't seem possible that the numbers can be right.  It invariably causes me to pick up the calculator and run the numbers.  The math never lies.  Here are a few of the better chronicles about compounding.

The Servant and the King
There was once a King who had a servant who was always very diligent in everything he did for the King.  The King enjoyed playing chess with the servant from time to time.  One time after playing chess the King was in a benevolent mood.   He offered to grant the servant any request he desired.  The servant demurred saying that he did not need anything. The King urged him to ask for something for his gratitude for his service.

The servant finally relented and told the King that he was a modest man and did not require much.  He would only ask that the King give him a grain of rice today on the first square on the chess board.  He then asked that the King give him two grains of rice the next day, four on the next day and continue to double the number of grains of rice on each succeeding square on the board.  The King quickly agreed and laughed to himself about how foolish the servant was.  He was prepared to give him something of real substance.

The grains of rice grew slowly but after a few weeks the King's financial advisor started to grow worried. The King's supply of rice was exhausted about half way through the 64 squares of the chess board.  They were now buying rice on the open market to settle the promise.  The financial advisor did a quick calculation of the amount required.  He told the King that it exceeded the entire value of the Kingdom by a thousand-fold.  The total number of rice grains...18,444,680,000,000,000,000!  The Servant ended up with the Kingdom.

The Indians and Manhattan Island
We all learned in history class that the Dutch bought Manhattan Island in 1626 for what is said to the equivalent of $24 in cloth and beads.  I remember thinking "what a steal".  This had to be one of the greatest purchases of all time.  I later learned about the "Rule of 72" which allows you to determine how long it takes for a sum to double at various rates of return.  Simply stated, your money will double in 10 years at 7.2% interest (72 divided by 7.2=10).  At 6% interest, it takes 12 years (72 divided by 6=12).   A 3% interest rate will take 24 years to double.

How much would the Indians have today if they had invested that $24 in 1626 and got a 7.2% annual return ?  Almost $10 trillion!  How does that compare to the value of Manhattan Island today?  I actually called the New York City Assessor's Office in 2000 to get that answer.  They told me that all of the real estate of Manhattan Island in that year had a total appraised value of only $125 billion and that included all of the buildings on it.  Even if we assume that real estate prices have doubled over the last 10 years (no way!) the Indians would have over 37 times as much money today if they had simply invested the money and let it compound.  At 6% the Indians would still have over $100 billion.  Real estate is not quite the investment you thought it was, is it?

Brutus and Caesar
Caesar was a great politician but like all politicians he had his share of enemies.  In order to insure that his children were taken care of if he met an early demise, he instructed Brutus to set up a trust for his children with $1,000 Roman dollars.  Of course, Brutus was not the most trustworthy guy.  He skimmed off a penny and set up a trust for his own heirs invested in safe government bonds yielding 3%.  Caesar's children got $999.99.  Brutus left  instructions that no one was to touch the money for 2,000 years.

How would that work out?  One cent compounded for 2,000 years at 3% would grow to $473,000,000,000,000,000,000,000 ( that is 473 billion billion).  The current GDP of the United States is about 15 trillion.  In other words, one single penny compounded for 2,000 years would be able to buy everything in the U.S. economy for the next 30 billion years.

If one penny could grow to that sum over the last 2,000 years why isn't there more wealth?  The biggest reason is that people rarely can keep their hands off the money.  Compounding only works if interest compounds on interest.  Most people can't do that.  They spend the income as soon as they earn it.

Another big reason is that the original investment capital is lost and the compounding stops with it.  Brutus thought he was being smart by investing in the safest investment around-government bonds.  Unfortunately, those bonds were Roman Empire bonds.  The empire fell apart and the government bonds became worthless.  Not only was the compound effect lost but so was the original penny.

Implications for Tomorrow
Consider the power of compounding as we look at our current government debt situation.  We owe almost $14.3 trillion in federal debt.  What was once a small snowball is becoming a gigantic boulder that has the potential to crush everything in its path.  Even if we don't add any more additional deficit spending to the snowball it is going to get bigger with each succeeding year just with the interest cost.  Of course, the current Obama budget will add an additional $1 trillion in new debt to the snowball plus the additional compounding effects.

That is why we have little choice but to act now.  We have a very small window of opportunity to avoid a lot of pain down the road.  Compound interest will bury us.  That is a mathematical certainty unless we stop the boulder or slow it down considerably.

If you want to get a good overview of the U.S. debt situation (and a whole lot more) go to for a scoreboard display of all the key statistics.

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