For most investors, success will depend on the power of compounding. (Of course, success might also derive from the luck to invest during a great bull market like 1982 - 1999.)
The rudiments of the joy of compounding can be found in what is called the rule of 70 (or sometimes the rule of 72). If you can earn 10% per year, divide 10 into 70 to find the "doubling time" is 7 years. This means with a 10% gain per year, an investment doubles every 7 years. Thus in 35 years an investment would double 5 times. Now remember this is doubling: 1 - 2 - 4 - 8 - 16 - 32. This would mean $1 invested at age 20, at 10%, would become $32 at age 55. This does ignore erratic growth rates and taxes. The rule also works to determine the rate of return required for a given "doubling time". If you want your money to double in 4 years, divide 70 by 4 to find the rate of return needed. The rule of 70 is sometimes quoted as the rule of 72, since 72 can be easily divided by a variety of numbers. So here, 72 divided by 4 is 18 and an 18% annual return is required to double your money every 4 years.
If you are interested in details, the rule of 70 should really be the rule of 69.3 or more precisely the rule of the natural logarithm of 2. A rule for tripling can be found from the natural logarithm of 3. But you can ignore the details and use the "rule of 70" guideline.
Now if you have ever talked to your grandmother or other older relatives, you have heard the flip side of the joy of compounding. The agony of compounding comes from the fact that inflation compounds in the same way that growth does. My grandmother bemoaned the price of everything and I sometimes have the same feeling as I remember 45 cents per pound of hamburger and 29 cents per gallon of gasoline. (My students could never guess why Motel 6 had its name: when the chain started a room was $6.) While investing, you need to recall growth rates after inflation are what really matter. As an extreme example, if inflation averaged 10% per year, the $1 that grew to $32 with a 10% growth rate, might be worth only $1.
Calculators have programs to perform a variety of interest and annuity calculations. Example: if you buy a 50 cent lottery ticket every day for 30 years, you spend $5,475. If you invested that money each day at 4% interest, you would end up with $10,585. At 8%, you would end up with $22,859 and at 12%, $54,106. However, I suspect that you will only appreciate the joy of compounding when your investments grow beyond your expectations.
In 1979 I first bought a mutual fund for my daughter under the Uniform Gift for Minors Act. In 1991 my daughter went off to college and we began to sell the fund. It was a good but not great fund. (I thought it would be a great fund when I bought it but you know how that goes.) We took out several times more money than I had put in and there was still money in the account. I then appreciated compounding in a way that I had not previously. You will of course notice the luck involved since this investment mostly grew during the great bull market 1982 - 1999. My daughter recognized the joy of compounding also; she started a Roth account in graduate school.
No matter what I say, I suspect you will need your own experience to appreciate the joy of compounding. But let me tell you one other personal experience that I still find stunning. I have more money than I earned. Think about that. If I add up my gross salary from 32 years of teaching, I have more money than that. You might suspect only the "Count" on Sesame Street or a Mathematics teacher would add up annual salaries. But I needed a spreadsheet to list tax-sheltered contributions in order to determine the maximum contribution and it was natural to sum the columns. (I also received a reminder of the power of compounding inflation: my earnings for the first full year I taught was $13,428.) When I compared the total of my earnings with my present worth, I could not believe the result. How could that happen? The answer is compounding and the bull market. (Yes, employer contributions helped also.)
Imagine then, two twin brothers with identical salaries. The first twin lives in a cave and eats berries and roots, never spending money on food, housing, or even taxes. He buries his salary in a hole in his cave under his rock slab mattress. The second twin lives a pleasant life, but is thrifty and saves and invests consistently (well, yes, during a bull market). The first twin probably starves to death or goes to prison for not paying his taxes. But anyway, the second twin ends up with more money because of the joy of compounding.
I have perhaps spent too much time describing compounding. CEO's and "fat cats" seem to have numerous ways to steal or make money. For most small investors, saving and compounding is the key to success.
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