The Magic of Compounding-Part I

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, which 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 have 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 paid the entire month’s salary up front on the first day of your employment, or, I will pay you 1 cent the first day. After that 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 1 cent coming to you. But on the second day you’ll earn 2 cents. Hold on, it gets better. On the 3rd 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 better 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 fellows who picked the penny-a-day plan are going to have at month’s end. Remember, on the one hand $1,000,000.00. On the other hand you get a penny the first day, two cents on the second day, 4 cents on the 3rd day, and 16 cents on the 5thday. If you keep working the numbers by the 15th day, you are up to $163.84. By the 18th day, you have cracked the $1,000 dollar mark coming in with $1310.72.

At this point you have to start thinking to yourself that it has taken 18 days, and I am only at $1300 and change. Was I better off taking the million dollars like the other day offered and taking a one million dollar lump sum payment? Maybe you were let’s see what happens. Keep in mind, we are continuing to double our money every day and we have 12 days to go.

On the 20th day, you are up to $5,242.88. Your numbers quickly move up from here on successive days:

Day 21 $10,485.76

Day 22 $20,971.52

Day 23 $41,943.04

Day 24 $83,886.08

Day 25 $167,772.16

Day 26 $335,544.32

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?

Day 27 $671,088.64

Day 28 $1,342,177.28

Day 29 $2,684,354.56

Day 30 $5,368,254.56

Day 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 the human mind thinks arithmetically, not exponentially. You might say that we are hardwired to think in this linear fashion. 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.

Start thinking exponentially, Make Money Now

Richard C. Stoyeck