Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.
– Albert Einstein
Near the beginning of his book, The Tipping Point; How Little Things Can Make a Big Difference, author Malcolm Gladwell asks the reader a seemingly simple question: imagine you can take a large piece of paper and fold it over once and then take that folded paper and fold it over again, and then again and again, until you have folded the original piece of paper 50 times…how tall would the final stack be?
As high as a phonebook?
As high as a fridge?
Get this: it would reach the sun.
Gladwell explains that in mathematical terms, this is known as geometric progression. “But human beings,” writes Gladwell, “have a hard time with this kind of progression because the end result—the effect—seems far out of proportion to the cause.”
If you’re like me, and everyone else I’ve posed this paper puzzle to, the answer seems preposterous. And even though Gladwell’s editors would’ve had to have checked the facts before going to publication, the cynic in me still didn’t believe the final answer as truth.
So I sat down one Friday night and ran the calculations for myself.
First, I googled the distance from the earth to the sun and discovered it to be 150 billion metres (93 million miles).
Then I jotted down the numbers 1 to 50 and started calculating. Since the original piece of paper is 1, if you fold that over once, you double it to 2. And if you fold that over, you’ve doubled that, so 2 x 2 = 4. Then if you fold that over, you hit 8 (4 x 2 = 8) and so on.
So in this case, the geometric progression is 2, 4, 8, 16, 32…with the common ratio being 2.
But here’s the thing: by the time I got only half-way through my calculations—i.e. the paper being folded 25 times—I was already at 33 million!
So I kept going and by the time I reached 38 folds of the paper, I’d hit 275 billion. And since the sun is 150 billion metres away, I had to admit that Malcolm Gladwell hadn’t lied to us.
And guess what another example of geometric progression is? Compound interest.
Over the years, I have experienced both sides of Einstein’s observation about compound interest:
“He who understands it, earns it. He who doesn’t, pays it.”
In other words, there is a huge difference between accumulating capital and paying down debt…and if you’re doing one, you’re probably not doing the other.
And as you likely know, capital trumps debt.
But don’t take my word for it. When it comes to compound interest, numbers speak far louder than words. Instead, here are a few figures to wrap your mind around:
Q: If you put aside a lump sum of $10,000 (and don’t add a cent more to it) and your investment yields an average 7% return per year, guess how much that $10,000 will be worth after 50 years (compounded quarterly)?
Q: If you put aside a lump sum of $10,000 and add $1000 per year to it, and your investment yields an average 7% return per year, guess how much you will have after 30 years (compounded quarterly)?
Q: If you put aside a lump sum of $5000 and add $2000 per year to it, and your investment yields an average 7% return per year, guess how much you will have after 50 years (compounded quarterly)?
A: $1.1 million
Paying Down Debt
Q: On the other side of the coin, if you have a $300,000 mortgage with a 5-year fixed closed rate of 3%, an amortization rate of 25 years and are paying the minimum monthly payment ($1400), guess how much interest you will pay on that mortgage over the 25 years?
A: $126,000 (ouch!)
Now, if you make a few small changes to the above $300,000 mortgage and negotiate a 5- year variable closed rate of 2.5%, an amortization rate of 20 years and pay accelerated weekly payments of $400, you will instead pay $72,000 in interest. That’s a big difference.
At least with mortgage debt, you’re investing in an asset that will hopefully go up in value over the years—and it’s a home for you to live in. But by making a few small changes to pay it down faster, you can certainly save a significant amount of interest, which means more money in your pocket.
Credit Card Debt
And let’s say you’re carrying a balance of $10,000 on your credit card and are paying it down $500 per month, assuming you don’t put any additional expenses on your card, at 17% (compounded daily), you will pay $1350 in interest in just one year. Yikes.
Compound interest really is magical…just try and make sure you are on the right side—the receiving side—of that magic more often than not!
Originally Published on Pink Gazelle