Last week we briefly went over the current events surrounding the surprising rise of cryptocurrencies. This week, we talk about Compound Interest a little more, away from the cryptocurrency market.
Eleventh Grade, High School Calculus, Mr. Shaw
“And the saddest part…really, the truly tragic, unbelievable thing is…”
Mr. Shaw pauses, shaking his head.
I sit on the front left row, across from my math teacher. He wears shabby black pants, a clean-pressed maroon polo shirt, and horn-rimmed spectacles. The shelves of our math room are littered with graffiti-filled textbooks.
Hanging on the wall right next to me is one of Mr. Shaw’s quirky prized possessions: a piece of paper filled down to the last millimeter, front and back, with microscopic notes. Every mathematical formula one can think of is written on it.
It is the leftovers of a procrastinating student who was allowed one page of notes for a test, and took it as a challenge to bring essentially the entire textbook on this scrap of paper.
Mr. Shaw has the page framed in a gold-trimmed picture case and protected behind glass. As young students in Mr. Shaw’s class, all we see in the crammed notes is a funny chance to laugh at ourselves over our desperate natures on test days, nothing more.
Today, though in his typical kind humor, Mr. Shaw is staring at the chalkboard with an unusual amount of frustration. He growls at us, “…Really, no matter how many times I say it…each and every year…not a single one of you listens.” And he bites his upper lip till the skin turns pale.
On the chalkboard is a drawing of an exponential equation, which we are supposed to be contemplating.
“You see,” he shouts, “At your age, if you’ll just start now…not tomorrow, not in ten years when you have a job, but now…it will be so easy for you. You’ll have no trouble at all. It’ll be a walk in the park.”
He started the calculus lesson discussing integrals and binomials, but wandered into the financial implications of exponential equations.
He stares at us now, hoping that we too will marvel at this picture of a line starting out flat at the left side of the graph, then slowly arching upwards as it moves to the right.
“Even just $100 a month into a Roth IRA would save you decades of your life when you’re my age,” he sighed. “…But alas…”
And he falls silent.
We all sit, staring at him, wondering what he expects us to say, and secretly stealing glances at the bell for lunch.
Fast forward almost twenty years, and I can proclaim him right on all accounts. Starting to save at the age of 17 would have provided years of freedom in my life, and I didn’t listen.
The Miracle of Compound Interest
That experience with Mr. Shaw is my earliest recollection of someone trying to explain to me the importance of Compound Interest.
Usually, these conversations revolve around finances–and rightfully so, since nowhere is Compound Interest so calculable as in finance, and so applicable to a modern human’s survival.
Compound Interest is much bigger than finance, however.
Let’s take a look at something interesting.
Let’s say you have a clean, brand new petri dish–those little plastic trays that a biologist uses to study how bacteria grows.
And let’s say you drop a bacterium in the center–just one, tiny, cell. It is so small, that you cannot see it with the naked eye, and it’s difficult to see even with a magnifying glass.
And let’s also say that this cell grows in the petri dish at a rate of doubling once per day. That is to say:
Day 1: 1 cell in the petri dish
Day 2: 2 cells
Day 3: 4 cells
Day 4: 8 cells
And so on.
Now, let’s take one assumption: On day 60 of this experiment, the number of cells will fill the entire petri dish down to every last nanometer, the resources of food all being consumed.
The whole petri dish will be perfectly full at that point. Kind of like this:
Let’s rewind back to day 55, a full five days before the experiment is over. Ask yourself this question:
How full is the petri dish at day 55?
Does this look about right?
If you said yes, you were wrong.
On day 55 of the experiment, with each cell doubling once per day, the petri dish would only be…about %3 full.
It would look more like this:
That’s right. On day 55, our petri dish with the doubling cells would like like the above.
And, once again, on day 60, it will look like the one below.
Like the student who procrastinated his studying until the very last moment for an exam, the exponential filling of the space appears right at the last possible moment.
In the student’s case, it is a crammed page of notes. In the petri dish’s space, it is the bacteria.
Don’t believe me? Try taking out a calculator.
Start with the number 100% for Day 60.
Divide that in half to find out where we were on Day 59. We get 50%.
Day 58: 25%
And so on, down to Day 55:
Crazy, isn’t it?
The Import of Compound Interest, Compounding in My Brain
This is the miracle of compound interest, and while I’ve been familiar with the concept of it since dear old Mr. Shaw explained it to me, I am only now beginning to comprehend its importance.
In fact, in a funny enough way, it’s almost as if the deserved attention of Compound Interest has been growing in my brain with such an exponential factor as above.
The first “bacterium” was placed in my brain at the age of 17 by Mr. Shaw.
In my mid-twenties I began to lightly think about it and do a little saving.
Two years ago I was saving a little bit pretty regularly, but not nearly enough, and just thought, “Gosh, I really should make it a bigger priority, but I’m so busy.”
One year ago I suddenly began trying to get our family affairs seriously in order.
This last week, my brain is all of a sudden exploding, the realization of Compound Interest bursting out my ears and eyeballs and splattering onto the napkins of the people sitting by me at the dinner table.
Once again, this post is getting long, so let’s continue the discussion next week.
p.s. For some of you, this may be a new thought, and for some of you reading this, you may have long since had this moment of realization. I would love to hear your stories and thoughts! Leave a comment below.