For those who want to climb the ladder of wealth, it is helpful to appreciate the unusual arithmetic by which money grows. Compound interest, described in a phrase of disputed origin, is “the eighth wonder of the world.” Wonder or trick, it has built great fortunes, and you can use it to get richer.
In 1944, the fifty-one-year-old IRS estate auditor Anne Scheiber left the organization that rewarded her for twenty-three years of distinguished service by never promoting her. Then she invested her savings of $5,000 in the stock market. Living frugally and studying companies, she continually reinvested her dividends. Her portfolio continued to grow until she died in 1995 at age 101. When her lawyer, Ben Clark, tried to meet with officials of Yeshiva University to tell them about a bequest she had left to the school, they had never heard of Anne Scheiber and wondered how to avoid wasting their time. But when the meeting was finally held, they learned that Ms. Scheiber was leaving them $22 million for the benefit of women students.
Were Anne Scheiber’s choices unusually lucky? How would an average investor have done? Taking the period from the start of 1944 until the end of 1997, allowing a couple of years for the settlement of the estate and the delivery of securities to Yeshiva, $5,000 invested in a large stock index grew to a mere $3.76 million; but the same amount invested in small stocks grew, on average, to $12.31 million. Starting with a little more than Anne, investing $8,936 instead of $5,000, the average small stock investor would have achieved her $22 million result.
Compound interest, or more accurately compound growth, is the process Anne Scheiber used, accumulating wealth by reinvesting her gains. An easy way to think about compound growth, and also about the ladder of wealth, is in terms of doubling and redoubling. Consider two investors, Sam Scared and Charlie Compounder. Suppose Sam Scared starts with $1; each time it doubles, he puts his $1 profit in a sock instead of reinvesting it. After ten doublings, Sam has a profit in the sock of $1 × 10 plus his original $1 for a total of $11. Charlie also starts with $1 and makes the same investments but lets his profit ride. His $1 becomes $2, $4, $8, et cetera, until after ten doublings he has $1,024. Sam’s wealth grows as $1, $2, $3…$11. This is called simple growth, arithmetic growth, or growth by addition. Charlie’s increases as $1, $2, $4…$1,024. This is known variously as compound, exponential, geometric, or multiplicative growth. Over a sufficiently long time, compound growth at a small rate will vastly exceed any rate of arithmetic growth, no matter how large! For instance, if Sam Scared made 100 percent a year and put it in a sock and Charlie Compounder made only 1 percent a year but reinvested it, Charlie’s wealth would eventually exceed Sam’s by as much as you please. This is true even if Sam started with far more than Charlie, even $1 billion to Charlie’s $1. Realizing this truth, Robert Malthus (1766–1834), believing that population grew geometrically and resources grew arithmetically, forecast increasingly great misery.
Politicians, dimly aware of the awesome power of compound growth, have in many jurisdictions passed laws against perpetuities to prevent the enormous concentrations of wealth that might arise from investments compounding without limit. On the other hand, some states and counties welcome perpetual trusts, being more interested in deriving revenue from them now.
The population of the world increased from 2.5 billion in 1930 to 7.3 billion in 2015, a growth rate of about 1 percent a year. It’s expected to reach 9.7 billion by 2050. Everyone knows that this can’t keep up; the carrying capacity of the earth—the amount of humanity the earth can support as limited by the available solar energy for food, and by other scarce resources—has been estimated as up to one hundred billion people. But what if we could somehow keep growing at, say, a rate of 1 percent a century? A calculation shows that in 1.2 million years we would be a solid sphere of flesh with a radius almost as large as that of our galaxy, expanding at the speed of light!
How fast do ordinary investments grow? The best simple long-term choice has been a broad common-stock index fund. At the average past growth rate of about 10 percent a year, such an investment has doubled in about 7.3 years. Historically, inflation offset about 3 percent of this, stretching to a little over a decade the average time required to double real buying power. Taxable investors in an index fund, which generates dividends and some realized capital gains, pay government another percent or so annually, delaying the doubling time to about twelve years.
To get quick approximate answers to compound interest problems like these, accountants have a handy trick called “the rule of 72.” It says: If money grows at a percentage R in each period then, with all gains reinvested, it will double in 72/R periods.
Example: Your money grows at 8 percent per year. If you reinvest your gains, how long does it take to double? By the rule of 72, it takes 72 ÷ 8 = 9 years, since a period in this example is one year.
Example: The net after-tax return from your market-neutral hedge fund averages 12 percent a year. You start with $1 million and reinvest your net profits. How much will you have in twenty-four years?
By the rule of 72, your money doubles in about six years. Then it doubles again in the next six years, and so forth, for 24 ÷ 6 = 4 doublings. So it multiplies by 2 × 2 × 2 × 2 = 16 and becomes $16 million. For more on the rule of 72, see appendix C.
The rule of 72 can expose outrageous claims. My personal trainer went to a stock market seminar where the operators were pitching a method called “rolling stocks.” Selecting common stocks that would supposedly oscillate between two levels, they advised the investor to repeatedly buy low and sell high. The operators claimed the suckers could make 22 percent a month. Why would they bother to share their secret when, by putting $2,000 in a tax-deferred IRA and reinvesting their gains, they would have more than $46 trillion in ten years?
Suppose you invest time and energy to add $1,000 to your wealth. Will you sacrifice as much to make another $1,000? And another? Economic theorists believe that most people won’t and that we typically put less value on each successive $1,000 increase in our net worth. We feel this way about all scarce useful items, or so-called economic goods. We value each additional unit less than the last.
I apply this to the trade-offs among health, wealth, and time. You can trade time and health to accumulate more wealth. Why health? You may be stressed, lose sleep, have a poor diet, or skip exercise. If you are like me and want better health, you can invest time and money on medical care, diagnostic and preventive measures, and exercise and fitness. For decades I have spent six to eight hours a week running, hiking, walking, playing tennis, and working out in a gym. I think of each hour spent on fitness as one day less that I’ll spend in a hospital. Or you can trade money for time by working less and buying goods and services that save time. Hire household help, a personal assistant, and pay other people to do things you don’t want to do. Thousand-dollar-an-hour New York professionals who pay $50 an hour for a car and driver so they can work while they commute understand clearly the monetary value of their time.
To get an idea of what your time is worth, take a moment now to think about how much you work and the income you get from your effort. Once you know your hourly rate you can identify situations where buying back some of your time is a bargain and other situations where you want to be selling more of your time. As you get used to thinking this way, I predict that you will often be surprised at how much you can gain.
Most people I’ve met haven’t thought through the comparative values to them of time, money, and health. Think of the single worker who spends two hours commuting forty miles from hot and smoggy Riverside, California, to a $25-an-hour job in balmy Newport Beach. If the worker moves from his $1,200-a-month apartment in Riverside to a comparable $2,500-a-month apartment in Newport Beach, his rent increases by $1,300 a month but he avoids forty hours of commuting. If his time is worth $25 per hour he would save $1,000 ($25 × 40) each month. Add to that the cost of driving his car an extra sixteen hundred miles. If his economical car costs him 50 cents a mile or $800 a month to operate, living in Newport Beach and saving forty hours’ driving time each month makes him $500 better off ($1,000 + $800 − $1,300). In effect he earned just $12.50 per hour during his commute. Does our worker figure this out? I suspect he does not, because the extra $1,300 a month in rent he would pay in Newport Beach is a clearly visible cost that is painfully and regularly inflicted, whereas the cost of his car is less evident and can be put out of mind.
Americans supposedly spend an average of forty or more hours a week watching television. Those who do have plenty of “junk time,” which they can use instead for an exercise or fitness program. Five hours a week for this can add five years of healthy life.
Undervaluing such a deferred benefit is a widespread investment error and seems to be part of our basic psychological makeup. A psychologist experimenting with four-year-olds offered each child one marshmallow, promising a second marshmallow if the first was still there when the experimenter returned to the room in twenty minutes. Left to their own devices, two-thirds of the children promptly ate their marshmallow and one-third waited to get two. Evaluating the children eight years later at age twelve, the testers found that the two-marshmallow children were markedly higher achievers than the one-marshmallow children. If you’re a one-marshmallow child who grew up to buy on credit at crushing rates of 16 percent to 29 percent annualized, and you ask me where to invest some free cash, the first thing I recommend is paying off your credit card debt. The interest is nondeductible and the saving is certain, so you’re earning a risk-free after-tax rate of 16 to 29 percent. The second thing I recommend is that you start investing some of your marshmallows, in order to enjoy more of them later, instead of gobbling them all immediately.