II. The Power of Compounding

Key take-aways

  1. The returns you generate this year earn their own returns next year. This is compounding.
  2. Compounding has dramatic effects on growing our money that we often don’t readily appreciate.
  3. The longer you have to invest, the more dramatic the compounding effect. So, the sooner you can start, the better.
  4. Even small improvements in annual returns make a big difference in growing your money over time.
135482271

Compounding is the key concept in how our money grows over time.  When we think about something growing, most of us think about “arithmetic” progress, that is 1, 2, 3, 4….  In investing, it is important to appreciate “geometric” growth, that is 1, 2, 4, 8….  Why do I say that?

Well, the return you make on your money this year earns its own return next year.  Here’s a simple example using round numbers.  If you invest $1,000 today and earn a 10% annual return, you have $1,100 in a year’s time.  If you earn a 10% return the following year, you don’t earn another $100, but rather $110, which is 10% of the $1,100 you have at the end of the first year. And so it goes…

Table 1: Compounding Math
 Start of Year 10% Return End of Year
Year 1 $1,000 100 $1,100
Year 2 $1,100 110 $1,210
Year 3 $1,210 121 $1,331
Year 4 $1,331 133 $1,464
Year 5 $1,464 146 $1,611
Year 6 $1,661 161 $1,772
Year 7 $1,772 177 $1,949

At the end of seven years, your money has not grown by 70%.  Rather, it has nearly doubled.  This is the power of compounding!  A fairly simple mathematical concept, but I emphasize it with excitement, because it has profound implications for investing.  Over long periods, the kind of time we have for retirement investing in particular, compounding has dramatic effects we often don’t readily appreciate.

The Impact of Longer Time Frames: the Earlier, the Better

Consider the graph below which illustrates how a one-time $1,000 investment grows over 45 years (for example, set aside at age 25 and invested until retirement at 70).  In this example, I use an annual return of 6.9%, which is the compound annual real return of the S&P 500 stock index from 1928 to 2016.(1)

Constancy Investors analysis: mathematical illustration
Constancy Investors analysis: mathematical illustration

At retirement, the account is now worth over 20x the original investment, over $20,000 in inflation-adjusted dollars.  Hardly chump change.  For more insight into this compounding effect, I introduce “The Rule of 72,” which is a rule of thumb used to estimate the time it takes for an investment to double, given its average annual return.  You divide 72 by the annual return, in this instance 6.9% (dropping the %), to get 10.  So, this investment doubles roughly every 10 years: 2x after 10 years, 4x after 20 years, 8x after 30 years, 16x after 40 years.  After 45 years, we see we are at 20x the original investment.  Not bad.

In practice, we do not set aside savings a single time and then kick back and watch it grow.  Rather, we save and invest some amount every year, or even every month or week.  And this is a much better practice.  Below is a graph of the same scenario, except instead of a once-only investment of $1,000, we invest $1,000 at the beginning of each year over the 45 years.

Constancy Investors analysis: mathematical illustration

The $45,000 invested ($1,000 per year over the 45 years) tallies to nearly $300,000 on the retirement date (again in today’s dollars), a tidy sum.  In this more “real world” illustration, the savings from the earliest years enjoy the most dramatic compounding effect and the savings from later years with less time, the least.  All in, the account is worth nearly 7x the amount contributed over your working lifetime.

You can already see from these two examples that the longer you have to invest, the more dramatic the compounding effect you enjoy (note the “hockey stick” shape as the bars grow).  Going back to the first example, if you had not 45, but only 35 investing years (set the $1,000 aside at age 35 instead of age 25), you’d have about $10,300 at retirement at age 70.  If you wanted to reach the same end goal of over $20,000 that you hit in the 45-year investing case but started 10 years later, you’d have to more than double your initial investment, to just over $2,000.  In the second example, if you started 10 years later, your annual contributions would have to grow from $1,000 to about $2,100 each year to reach the same $300,000 amount at retirement.

Here are the important lessons so far.  Over time, due to compounding, money saved and invested well can grow dramatically.  The longer you have to invest, the more dramatic the compounding effect.  So, the sooner you can start, the better.

The Impact of Higher Returns: Small Improvement, Big Difference

There is one more important point to make.  What happens if the return we make changes?  Let’s examine this question as optimists and assume our return is a percentage point higher than in the illustrations above, so 7.9% average annual return instead of 6.9%.  Below are repeats of our first two graphs—one-time $1,000 investment and $1,000 investments each year, in both cases over 45 years—with just one slight change, now earning an 7.9% annual return.

Constancy Investors analysis: mathematical illustration

With this one percentage point improvement in our average annual return, our $1,000 one-time investment grows to nearly $31,000 after 45 years.  This compares to just over $20,000 in our 6.9% return case.  Quite a difference!

Constancy Investors analysis: mathematical illustration
Constancy Investors analysis: mathematical illustration

Investing $1,000 a year for 45 years, with a 7.9% annual return, results in nearly $410,000 at retirement.  This is nearly $110,000 more at retirement compared to the equivalent 6.9% scenario.  Now we are starting to talk about some real money!

So, with respect to compounding, here is the final insight to keep in mind for successful long-term investing.  Even small improvements in annual returns make a big difference over time.

(1) Source: Standard & Poor’s.  The S&P 500 is an index that includes approximately 500 of the largest publicly-traded companies in the United States.  It is the most commonly used measure of the U.S. stock market.  The total real return for the S&P 500 averaged 6.9% per year (compound average or geometric average) for the period 1928-2016.  Real return means after taking into account inflation (after the bite that inflation takes out of stated returns), so the increase reflects growth in today’s dollars.