# Let’s talk about exponential growth

Assume that in a lake the population of lily pads doubles its size every day. If it takes 48 days to cover the entire lake, how long it took to cover half the lake?

24 days … is not the right answer, give it another try…

Bingo!

If it doubles the size every day it probably covered half the lake by day 47, and on day 46 only one quarter.

This little exercise, in addition to jump start your system 2, is useful to illustrate the principle of exponential growth. Previously, I have talked about the power of compound interest, and in part they are closely related concepts.

“If you can’t explain it simply, you don’t understand it well enough”

#### How can we have a better understanding of this phenomenon?

Suppose that with \$100 you buy 10 apples which you can sell in \$12 each. If you sell all of them, you will have earned \$120 or a 20 percent gain. Now you have two choices: invest the total \$120 or just \$100 and spend / withdraw your \$20 gain.

#### You see where we’re heading …

With \$120, you could buy 12 apples for \$10 each, and you could get \$144 for the sale of this dozen, your profit on the \$120 invested in this second round would amount to \$24 or 20 percent, but bearing in mind that your initial investment was \$100 you can consider your total return to be \$44.

Under the scenario of investing only \$100, your profit in this second round would again be \$20, and the accumulated profit would reach \$40.

While a mere \$4 difference may not be enough to justify a risk of reinvestment, how would it change if instead of two rounds we wait for five or even 10? After five repetitions, the scenario where all is invested would accumulate \$249 and an effective yield of 149 percent, against a final value of \$200 and an effective yield of 100 percent.

#### Are you not convinced yet?

After ten laps, the value of the compounding portfolio doubles the size of the non-compounding one (\$619 vs. \$300) with an effective yield of 519 percent against a 200.

#### Now, after this brief example, how can I partake in the compound interest story?

One of the differences between the two approaches was to remain invested, to stay in. We understand that cash requirements or contingent needs often arise, but the effect of these outflows in the long run can be large, depending primarily on the timing. Withdrawing \$20 of your profits in year one would impact the result by almost \$100, if you take out \$20 in year five the damage reaches \$49 and by year 10 withdrawing \$20 yields a mere \$20 downturn.

As you see, from the example, many of the companies that you know today, achieved a significant size after being able to capitalize (remain invested) the profits (yield) to provide goods or services in a proper and profitable fashion.

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