Mathematical Concept Highlights Importance of Compound Interest

Understanding compound interest — or more simply —compounding, is at the heart of financial basics. Ever wonder how long it will take your 401(k) to double given a specific rate of return? Or what rate of return you would need to achieve for your investment to double in five years?
 
Compounding can be no better or basically illustrated than the “Rule of 72.” The Rule of 72 is a handy tool that can be used to approximate the amount of time it will take for something, e.g., money, to double. Practically speaking, this concept is well-suited for understanding investments, for example:

  • Your 401(k) earning 6% per year will take 12 years to double: 72 divided by 6 equals 12 
  • An investment of $1,000 will double to $2,000 in eight years if it grows at 9% per year: 72 divided by 8 = 9%
  • A savings account earning 0.5% will double in 144 years! 72 divided by 0.5 = 144 years (Yikes!)

This concept works beyond investments:

  • If the United States gross domestic product can grow at 4%, then the economy will double in 18 years: 72 divided by 4 = 18
  • But it will take the U.S. economy 36 years to double if it grows at 2%: 72 divided by 36 = 2

Interest Rates and Compounding

The difference even a small change in interest rates can have on how quickly whatever you’re measuring will double is key to understanding compounding. In the example above, the difference between 2% and 4% translates to an 18-year difference in how long it takes for an economy to double. It starts to make sense that politicians spend so much time taking about how the economy is growing.

To drive home the concept further, an economy growing at 4% will have doubled twice in the same time period it took the economy growing at 2% to double.You can get creative in how you apply this principle: the growth of population or inflation, the spread of a virus or a video, etc.
  • College tuition growing at 8% means the cost will double in nine years. At that rate, by the time a child born today is ready to attend college, tuition will have increased fourfold!
  • A company’s bottom line that grows at 10% will see earnings double in 7.2 years; when a company’s earnings increase at 5%, its profit takes 14.4 years to double.

The second example makes it clear why one would be willing to pay more on a price-earnings basis for the faster-growing companies. This concept also illustrates why technology companies with strong balance sheets and high earnings-growth rates trade at higher profit multiples than other more steady, slower-growth utility businesses.

You Don't Have to Be an Einstein to Get This

Hopefully this concept highlights the importance of compounding. Compounding favors those who start early: Saving in your 20s gives those monies time to double potentially three or four times before retirement. Said another way, $1,000 invested at age 20, earning 7.2%, increases to $2,000 by age 30. Maybe this doesn’t seem all that special. But follow that investment a few decades further, assuming the same rate of return, that $2,000 increases to $4,000 by 40, $8,000 by 50 and $16,000 by 60.

There is a reason Albert Einstein is credited with saying: “Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.” 


Who wants to argue with that?

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This article was originally published in the October 2020 issue of BetterInvesting Magazine.

Matt Mondoux sits on the investment committee and is an adviser at Blue Chip Partners,Inc., a privately owned, registered investment advi­sory firm based in Farmington Hills, Michigan. Visit www.bluechippartners.com.

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