The Magic of Compounding

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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 nuts're 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	$0.04
4	$0.08
5	$0.16
6	$0.32
7	$0.64
8	$1.28

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.

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	$1,310.72
19	$2,621.44
20	$5,242.88

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	$671,088.64
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.

The New Slant
Really understanding compounding will make all the difference in investing. I believe that Warren Buffet, the world's greatest investor, is hardwired to think geometrically. He is rich beyond belief because he totally gets the magic of compounding and he executes on the concept. I am going to get these numbers wrong because I'm doing them from memory but it doesn't matter, you'll get the concept. Buffett started a partnership way back when. He had a number of limited partners invest with him and he took a percentage of the gains. In the late 1960s he terminated the partnership with his famous letter, "When you no longer understand the way the game is played, it's time to leave the game." I'm paraphrasing, even though it's in quotes.

Buffett took about $100 million out of that first partnership for himself, so he was working with $100 million, keep that in mind. In 1974 when the bear market bottomed, it might have been early 1975, he started another rise...he took over Berkshire Hathaway. Buffet, since the 1970's, has been getting a compounded (remember that means exponential) growth rate of about 22 to 24%.

This is where I introduce you to The Magic of Compounding's cousin, The Rule of 72. With the Rule of 72 you can calculate how long it will take you to double your money at any given rate of return. OK? So for example, if you're earning 12% on your money and you want to know how long it will take to double it (we're compounding, remember?) divide 72 by 12 and your answer is 6, it will take 6 years to double your money. Do another one. If you're getting 6% on your money, divide 72 by 6 and you'll see that it will take 12 years to double. If you're getting 9%, it's 72 divided by 9, or 8 years to double up.

So for Warren B., he's getting 22% on his money. That means he divides 72 by 22 and sees that, gee, in only 3.27 years, or every 3 years and 4 months, he doubles his money. Since he's been at it about 25 years with that $100 million he had to play with, he's doubled his original $100 million about seven times (25 years dividend by a double every 3 years and 4 months equals 7.69, or let's go with seven even doubles). Remember now, he's not making 7 times his money with the $100 million, that would be an arithmetic progression that would give him $700 million. He's making seven doubles, a geometric or compounded progression.

Let's see how that works.

Warren Buffet's Geometric Progression

Starting Dollar Amount: $100 million Time Periods Involved: Seven 3 year and 4 month periods

Period	Time Taken	Compounded Gain
0	Starting Point	$100,000,000
1	3 years 4 months later	$200,000,000
2	6 years 8 months later	$400,000,000
3	10 years later	$800,000,000
4	13 years 4 months later	$1,600,000,000
5	16 years 8 months later	$3,200,000,000
6	20 years later	$6,400,000,000
7	23 years 4 months later	$12,800,000,000

I believe Buffett is worth about $15 billion, it could be $20 billion at this point. It doesn't matter, he is somewhere in his eighth double. This is the magic of compounding! Also, he never sells. That means his money is doubling every three years and four months with no tax consequences. He gets taxed only when he sells. The money compounds until he dies, then it's taxed at a capital gains rate in the far distant future. Buffett could not sell if he wanted to because emotionally he can't bring himself to stop the compounding effect.

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 Buffett concept, or classical Graham and Dodd analysis. In the mean time, good luck with understanding the magic of compounding and good luck with Stocksatbottom.com.

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Richard Stoyeck became one of America’s leading money managers and financial advisors. He has appeared on all major financial television shows (CNBC, Bloomberg’s, ABC’s Finance Tonight, and CBS’s Morning News Round-Up) and is quoted constantly in the Wall Street Journal, Barron’s, and the New York Times. He received his post-graduate education at Harvard University. He was Lehman’s Brothers youngest Senior Vice President at 28, and a Limited Partner at Bear Stearns at 31. If you want the same stock market returns he generates for members of the Forbes 400, then do what thousands of subscribers before you have done.