 # Exponential Growth is a Double-Edged Sword

The COVID case count has been growing exponentially in recent weeks. Are you unclear on what that means or do you cringe at the memory of old high school algebra word problems? If so, I’ll explain exponential growth.

First, a note on semantics.

• Compound growth, geometric growth, and exponential growth are synonymous terms.
• The term growing exponentially is often used to connote something growing quickly. Not necessarily true. For example, if your savings account offers 0.1% interest, that’s exponential growth but it’s not fast growth by any measure.

Exponential growth simply means that a value is growing by a constant percentage for each period. The growth rate is added to one and the value from the previous period is multiplied by that factor to get the next period’s value.

A simple example may help:

• Assume there are 100 new COVID cases today and the current growth rate is 20% per week.
• The growth factor is 1.2. At that rate, there will be 120 new cases next week and 144 in two weeks (not 140). To get next week’s number, multiply the current week by 1.2.
• In week 3, there will be 173; in week 4, there will be 207; and by week 5, there are 249 new cases. That’s the “magic” in exponential growth – the number of new cases grows faster each week even though the percentage growth rate is constant.

Fast exponential growth is great for your IRA, not so good in a pandemic. Masks, distancing, and vaccines all reduce the growth rate.

Here’s a good trick for your next Zoom cocktail party. If you know the growth rate and want to know how many time periods it takes for something to double, you can try to remember logarithms from high school or you can simply use the rule of 72:

• Divide the growth rate (e.g., 20%) into 72; the answer is a very close estimate for the number of time periods it will take for something to double at that rate of growth.
• If you’re wondering, at 20% weekly growth, the new COVID case rate doubles in ~3.8 weeks (the rule of 72 predicts 3.6 weeks).
• Alternatively, if you have an IRA that is averaging 6% annual returns and you’re neither contributing to it nor taking distributions, its value will double in ~12 years.
• Or, that money sitting in your savings account earning 0.1%? It will double in ~693 years!

Wear a mask and skip the extended family Thanksgiving gathering; your IRA growth rate won’t slow down but new COVID cases will.

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