Compounding Away – Twice The Time ≠ Twice The Results

“Exponentials can’t go on forever, because they will gobble up everything.” — Carl Sagan

When people talk about how amazing the “compound effect” is, I ask them to explain the concept.

Inevitably one of two stories pops up.

The first one is the story of the water lily which doubles its population in the pond every day. On day one there’s just one, day two there’s two. By day 29 they covers half the pond, the next day they’re going to cover the whole damn thing. When people recount this story I explain that it’s a math problem, and has no basis in how water lilies actually grow.

The second is a (apocryphal) story about the inventor of chess who, wanting to show Shihram, the King of India, how important all his people are, invents the game. Shihram’s so impressed by this that he offers the inventor endless riches.

However, the inventor says he only had one request, that Shihram begin by placing one grain of wheat on the first square on the board, two on the second and keep doubling the amount of grain until he reaches the 64th square.

Shihram promptly orders his servants to begin the task. After a while one of the servants approaches Shihram and says they can’t do it. When Shihram asks why the servant explains that all the wheat in his kingdom, or anywhere else, isn’t enough to fulfill the wish.

When you do the math you realize that, with the compound effect at work, it would mean a total of about 18,446,744 trillion (18,446,744,000,000,000,000) grains of wheat. To put it in perspective 1 kilogram (2.2 pounds) is only about 15,000 grains.

That’s all well and good, but when do you see anything like this occur in real life?

You don’t. Sure, in the initial stages you might see it, but it’s usually only applicable within very limited areas. Every pond has its boundaries.

Myth busted!

I don’t tell people this to burst their bubble, but the way the compound effect is being portrayed isn’t very practical. Also, it sets people up for disappointment.

Let’s look at a better example: Saving money.

Let’s say you manage to get a savings account with a 3% interest per year. You save an initial \$1200 the first year and just watch it grow over the next 10 years. A person who’s heard the previous examples of the compound effect will naturally expect this to pay huge dividends. In reality it’ll look something like this:

• Y1: \$1 200
• Y2: \$1 236
• Y3: \$1 273
• Y4: \$1 311
• Y5: \$1 351
• Y6: \$1 391
• Y7: \$1 433
• Y8: \$1 476
• Y9: \$1 520
• Y10: \$1 566

It compounds. You build interest on the previous year’s interest. It’s something, but it’s not the exponential growth we’d like to see. Definitely not the way it’s illustrated in the stories from before.

Let’s say you save up \$1200 every year to add to it. This is also a more realistic outlook on how you can assist the compound effect and harness its potential. What would that look like?

• Y1: \$1 200
• Y2: \$2 436
• Y3: \$3 709
• Y4: \$5 020
• Y5: \$6 371
• Y6: \$7 762
• Y7: \$9 195
• Y8: \$10 671
• Y9: \$12 191
• Y10: \$13 757

Now we’re actually seeing a real difference already by year 2, you’ve almost matched the amount you would’ve saved by year 10.

So, you get a raise every year. What happens if you increase the amount you put into your savings account by just 5% every year compared to the year before?

• Y1: \$1 200
• Y2: \$2 496
• Y3: \$3 896
• Y4: \$5 407
• Y5: \$7 040
• Y6: \$8 803
• Y7: \$10 707
• Y8: \$12 764
• Y9: \$14 985
• Y10: \$17 384

You don’t notice much difference during the first 5 years but by year 7 your savings are 1 year ahead of the previous example.

This is not a huge difference by any means, but it illustrates a more realistic and practical view of what the compound effect actually looks like in our everyday lives.

What if the thing you want to improve on isn’t something that has a measurable interest? Something that’s more static, like reading a book or practicing an instrument?

Well, there are still things you can measure. Like the amount of pages or hours spent practicing.

Before we get into that, ask yourself: Is dedicating 5 hours, 1 day a week to it really your best option? Or could you benefit more in the long run by making it a habit?

Then ask yourself what the minimum amount of pages you can read or time you can put aside for practice is.

Let’s say you read 10 pages a day, 5 days a week during your lunch break. Well, after 1 week you’ve racked up 50 pages. It’s not much, but after about a month and a half you’ve read one book. That makes a total of 6 books per year. Given that the average person reads 4 books per year, you’re already 2 books ahead.

If you manage to get in just 45 minutes of practice 5 days a week after work, it might not seem like much at first. But in one year you will have racked up almost 200 hours of practice in total.

While reading and practicing that much is both realistic and great, it’s not just about quantity. It’s also a matter of reading books you enjoy, and making the practice purposeful.

It’s not just about ticking the boxes, it’s also making sure that it’s worth your investment.

The question now is: Where are you going to put the compound effect to work in your life?