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Another one Einstein got right: Compound interest

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Albert Einstein famously cited compound interest as one of the wonders of the world, and thousands of articles and books have been written on that topic over the years.

This time I’m taking a slightly different approach. I want to give you some examples that should be highly relevant to all investors. In a follow-up column, I will show how you can make these numbers work for you, no matter what your age.

In a second follow-up piece, I will discuss how you can turn some of this information into amazing results for a child, a grandchild or some other young person. Because Einstein was right. Again.

Time is the pearl

The basis of all this is compound interest, which as you know combines growth with time. The more growth, the higher is the ultimate reward. The more time, the higher the ultimate reward. Time, as we shall see, is the real pearl.

From an investor’s point of view, let’s start with the modest long-term growth rate of 4%. Actually, this is a fairly conservative estimate for bond investors. Since 1928, long-term corporate bonds have compounded at 6.1%; U.S. government bonds have compounded at 5.7%.

Growth of 4% won’t set the world on fire, at least not quickly. If you start with $1,000 (I’ll use that figure in all of my examples in this column), after 20 years your money will slightly more than double, to $2,191. If you double the period to 40 years, that initial $1,000 grows to $4,801.

In the following table you’ll find those numbers plus the results for three longer periods.

Growth of $1,000 at 4%

Years Ending value
20       $2,191
40       $4,801
60       $10,520
80       $23,050
100     $50,505
I believe that most investors with a really-long-term view will be willing to take on some additional risk in order to seek more growth than that. Depending on its allocation between bonds and equities, a balanced portfolio with proper equity diversification should provide long-term growth in the range of 6% to 8%.

Let’s see what that would do over time with a series of comparisons. As you’ll see, the difference between 6% and 8% gets much more dramatic over longer periods.

Growth of $1,000 over 20 years at 6% and 8%

6% return $3,207
8% return $4,661
Growth of $1,000 over 40 years at 6% and 8%

6% return $10,286
8% return $21,725
Growth of $1,000 over 60 years at 6% and 8%

6% return $32,988
8% return $101,257
Growth of $1,000 over 80 years at 6% and 8%

6% return $105,706
8% return $477,594
Growth of $1,000 over 100 years at 6% and 8%

6% return $339,302
8% return $2,199,761
Remember, those long-term results come from an allocation with only moderate levels of risk.

The benefits of an all-equities portfolio

It gets better for long-term investors who are willing to invest in an all-equity portfolio. The U.S. stock market, measured by the S&P 500 Index, has a very long history of returning about 10%. Particularly for an all-equity portfolio that’s diversified beyond those 500 stocks, I think 10% is a reasonable long-term expectation.

Here’s a table to show how 10% would compound over increasingly long periods.

Growth of $1,000 at 10%

Years Ending value
20      $6,728
40      $45,259
60      $304,488
80      $2,048,400
100   $13,780,612
I think those numbers are amazing, considering that this started with a single investment of only $1,000.

We’re not quite done with this lesson in compound interest. Next, I’ll show you what happens to a portfolio that compounds at 12%.

Any savvy investor is likely to recognize at once that 12% is a pretty high expectation. But the evidence of history indicates this is reasonable — even conservative — for investors who stay the course in small-cap value stocks.

Growth of $1,000 at 12%

Years Ending value
20      $9,646
40      $93,051
60      $897,597
80      $8,658,483
100    $83,522,265
A 12% return may be hard to swallow. But academic studies indicate that the U.S. small-cap value index has compounded at 13.6% since 1928. I studied the numbers myself and found that in every period of 65 years or longer, small-cap value outperformed the S&P 500 by a significant factor.

It’s highly unlikely anybody reading this column will ever turn $1,000 into $83 million. My point here is to show what can happen over very long periods of time from growth levels that are reasonable to expect.

If you don’t remember anything else from these tables I hope you’ll remember the great benefit of time — the most precious resource that many investors have.

In my next column, I’ll discuss how you can apply this information to your own situation.

Richard Buck contributed to this article.