The Magic of Compounding

By: Richard Stoyeck
Submitted: 2007-01-17 16:17:05
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Some of you know about this, some of you don't. Either way I'm going to give you the basics of compounding, plus a couple of new slants on the concept. I suggest you read The Magic of Compounding not just once, but several times. If you have children, print this write-up and give it to them to read. If they master this concept they will become rich.

The Basics

Compounding describes how numbers, or money, can grow. Numbers can grow in an arithmetic progression, for example 2,4,6,8,10,12 or 3,6,9,12,15,18, where one unit is added on at each step in the progression and that action provides the growth, or, numbers can grow exponentially, 2,4,8,16,32,64. In an exponential progression the increase comes by doubling the number at each step in the progression. See the difference? This is compounding.

Now the really amazing part, the magic, comes when you see how fast compounding will make money grow. And guess what! That's right, I've got a little game to play with you, a little story to tell, that will illustrate this principle. This puzzle is as old as J.P. Morgan's moustache comb, so if you've already been schooled in compounding you've heard it before. But didn't I tell you to read this section several times? OK, then, solve the puzzle with us once more while I tell it for the first time to the children for whom "The Magic of Compounding" has just been printed out.

The Puzzle

I'm a wealthy and generous man, and I want to hire you to work for me for one month. Since I'm also flexible, I give you a choice: you can choose to be payed the entire month's salary up front on the first day of your employment, or, I will pay you 1 cent the first day and I'll double your pay every day for the rest of the month, but you won't get the money until the last day of the month. So on the first day you'll work 8 whole hours and you'll have 1cent coming to you. But on the second day you'll earn 2cents. Hold on, it gets better, the 3rd day with me you'll have earned 4 cents, the day after that 8 cents and so on. Saturdays and Sundays are included just to give you a chance. Oh, by the way, if you take your pay all at once on the first day I'll give you a million bucks ($1,000,000.00) cash. Seems like an easy choice, doesn't it?

Well, you decide for yourself . Now let's look at how much the individual who picked the penney-a-day plan are going to have at month's end. Remember, on the one hand $1,000,000.00. On the other hand:

Day  Amount 
 1        $ 0.01
 2        $ 0.02
 3        S 0.04
 4        $ 0.08
 5        $ 0.16
 6        $ 0.32
 7        $ 0.64
 8        $ 0.28

Hey folks, it's day eight, you're up to $1.28 and you only have a month. Maybe you are better off taking the one shot deal, the million dollars.

Let's see what happens:

Day  Amount 
 9        $ 2.56
 10      $ 5.12
 11      $ 10.24
 12      $ 20.48
 13      $ 40.96
 14      $ 81.82
 15      $ 163.84
 16      $ 327.68
 17      $ 655.36
 18      $ 1310.72
 19      $ 2621.44
 20      $ 5242.88

By the way, did any of you ask me what month of the year we're in? Is it February with 28 days, or leap year with 29 days, or September with 30 days, or December with 31 days? You should realize that it's going to make a difference. Do you want the million dollars? Ask your kids again which they would choose?

Let's continue:

Day Amount 
 21     $ 10,485.76
 22     $ 20,971.52
 23     $ 41,943.04
 24     $ 83,886.08
 25     $ 167,772.16
 26     $ 335,544.32
 27     $ 671,772.16
 28     $ 1,342,177.28
 29     $ 2,684,354.56
 30     $ 5,368,709.12
 31     $ 10,737,418.24

If you work for me in September with 30 days you make over $5,000,000. In December it's over $10,000,000! I have never met the child who didn't leap at the $1,000,000 on day one. This is because human brains think arithmetically, not exponentially. You might say that we are hardwired to think in this linear way, that the software in our brains compels us to think about progressions as being simple arithmetic ones. Luckily though, how we think about things, our prejudices, our attitudes, and our mindsets, can all be changed and worked with. We can update the software! We can consciously change the way we think about numbers, money and investing by absorbing new information, namely, that when you make your money compound you can get rich sooner rather than later.

Teach your children to live a balanced life, and also help them master this concept and you will have very happy and very rich children. In stocks I show you how to make money at the bottom by buying depressed securities that are going to come right back, making you a fortune as they rocket off the bottom. In the future I will also show you how to make money with the Warren Buffet concept, or classical Graham and Dodd analysis. In the mean time, good luck with understanding the magic of compounding.

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