The Little Money Book

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Chapter 12: Money from Money

– Casino Royale (2006)

This chapter is about making money without working. (Applause!) How? By buying things that you expect will make a profit—in other words, by investing. Almost anything you buy with a plan to sell it for more than you paid can be an investment. In this book we will focus on the main types of financial investments, stocks and bonds.

The profit you make from an investment is its *return*. Often there are two parts of return: one is *yield*, which are regular payments such as *interest *from a bond or *dividends *from a stock; the second is *capital gains*, which are the profits from selling something for a higher price than you bought it for. Capital gains are *unrealized *if the value has increased but you have not yet sold. They can shrink or even become *capital losses* if the price of the thing goes down. Capital gains are *realized *once you’ve sold. Add up yield and capital gains and you get *total return*.

The total return of an investment is reduced by *investment expenses*. Investment expenses are, pick your adjective, pernicious, insidious, sneaky. They seem harmless. They are often expressed as a small percentage of the amount in your account. It’s not uncommon to see expenses of 1% of your account balance each year. And you might say, “Oh, 1% isn’t a whole lot.” But look at this example:

If you had been able to invest $5,000 in the S&P 500 stock index at the end of 1990, the total return of the index without paying any expenses over the next thirty years would have increased the value to $105,532 by the end of 2020.

If you had paid someone 1% of your account every year to “manage” your investment you’d only have $80,381. Ugh!

Investment expenses are one of the few things about investing you actually control. These days there are many options to keep them below 0.25%, or even below 0.1%.

There is very little that any investment manager or advisor does to justify skimming a quarter of your retirement money off the top.

What is going on in this example? Why does 1% make such a difference over a long time? The reason is that investment returns *compound*. Compounding means that the investment income you earn in one period earns returns in all the following periods.

Bear with me for just a little math…

If I deposit $100 in account and earn 10% annual interest [25a], in a year I will have $110 ($100 x 1.1). If I stay invested another year, that $110 will turn into $121 ($100 x 1.1 x 1.1, which is the same as $100 x (1.1)^2). Notice that in the second year I earned interest on the interest I earned in the first year. Each period I multiply my money by one plus the interest rate. Do this over thirty years and you get $100 x (1.1)^30, which equals $1,745.

Now take one percent off the interest rate for investment expenses. After one year I have $109 ($100 x 1.09). Just a dollar less than with no expenses. But after thirty years I have $100 x (1.09)^30, which equals $1,327. That’s 24% less money than with no expenses.

Some financial products only offer simple interest. With simple interest you earn the same amount each period, based on the original deposit. Simple interest is not multiplied, it’s just *added*. The first year of simple interest is the same as with compound interest: $100 + $10 = $110. In year two you start to fall behind: $100 + $10 + $10 = $120. Not much of a difference at first. But look at what happens over thirty years: $100 + $10 + $10 + $10…etc. = $400. By the time you reach thirty years, 10% simple interest is the equivalent of just 0.3% compound interest. Here is a picture:

What are the takeaways?

- The power of compounding comes over time. Notice it’s not until after about five years that the lines diverge.
- A small difference in return costs you big.
- Simple interest sucks.

Sometimes it’s helpful to turn the calculation around. Go back to the earlier illustration of investing $5,000 in the S&P 500 stock index in 1990. That initial dollar amount grew by some compound return to reach $105,532. We need to find the rate,* r*, that solves the equation $5,000 x (1 + *r*)^30 = $105,532. A little algebra and a calculator will tell you that *r* =10.7%. This is the annual compound return of the S&P 500 over the thirty years ending in 2020.

Let’s return to the simple example from Chapter 2. Recall we earned annual income of $60,000 over forty-five working years, or a total of $2,700,000. What if right away we start saving $500 a month for retirement? We’ll sock away $270,000 in total (a 10% savings rate). Now if we earn an average of 5% a year by investing, we accumulate $1,017,441 by the time we are ready to retire at age sixty-five. [26]

What if we start saving later? Even if we save the same total amount, $270,000, by increasing our monthly contribution to $643, we won’t do nearly as well. As you can see in the table below, our “money pile” at age sixty-five is now just $733,388. And so on: start later and accumulate much less *even when saving the exact same amount*.

20

$500

45

$1,017,441

30

$643

35

$733,388

40

$900

25

$538,192

50

$1,500

15

$402,604

I hope this convinces you of the power of compounding, and the importance of starting to save early. And of course, we each get only one chance to start early. When she’s gone, she’s gone.

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Compounding Explained

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