Compound interest is one of those ideas that doesn’t come easily. Some of that seems to be a direct result of the way that we’re mathematically conditioned to see the world. It’s something that we should talk more about.

Small Things…build up

Most of my non-work life is taken up by trying to restart exercising, checking facebook to see if anyone has like my last status update, worrying about the size of my twitter following, seeing how many more people have read today’s blog post since I last checked an hour ago, and panicking about any tax return deadlines that I may have missed.

It is a long and steady flow of small anxieties.

The thing about small things is that they eventually grow into big things. Game-changingly so. For example, my steady trickle of panic may one day become a coronary. Or a lifelong commitment to an asylum. Or an inability to leave the house without locking the door four times and high-fiving the gutter. All possible.


Using this same principle, I could probably also make small changes, and achieve small successes, and hope for similarly grand potentials of outcome. You know the old adage: “a lifetime to build a reputation”?

Financial freedom is no different. For most people, it does not arrive with a bonus, or a career opportunity. There is no lotto win, or fortuitous marriage into inheritance. High income earners, as well as the poor, can get stuck in the trap of not enough money*: that moment where the cash coming in does not cover the cash going out. At which point: credit cards are maxed, home loans extended, second mortgage applications submitted, relatives approached, et cetera.
*The ‘wealthy’ man with the four kids in private schools and the two homes on mortgage and the wife with the retail habit – he too can go into convulsive fits of panic in the week before pay day. 

The Solution?

The solution involves two things, really:

  • regular small sacrifices; and
  • time (or, rather, patience – which, in this case, is roughly the same thing).

From what I have seen (in myself, and in others), the reason we fail on this front is that our default mental math position is addition rather than multiplication. We look at the small sacrifices as an additive process of pain, rather than a multiplicative organic process of future rewards.

The Compound Interest Crisis of Mathematical Conditioning

My guess is that our perception of time (and life!) as addition and subtraction has real implications for the way that we operate. Relationships built on grand gestures seem to have greater standing than those forged with small but repeated acts of kindness. We shout at a subordinate when we’re having a bad day, because we can tally it up against all those times that we’ve been gracious. We don’t recycle because what’s the point if no one else is doing it.

The trouble is that life and/or reality is an exponential process. Small shifts have multiplier effects. And if you ever have the chance, you should read Alex Bellos’ “Here’s Looking At Euclid*” – because in it, he explores the psychology of math.
*Also called “Alex’s Adventures in Numberland”. There seems to have been an argument between the American and Rest-of-the-World publishers about what title the book would be published under…

In the very first chapter, he studies the Munduruku tribe of Brazil, who have no words for numbers beyond “five” (ie. their number system goes 1, 2, 3, 4ish, a-bit-more-than-4ish, many). He talks about experiments that were run to understand their understanding of magnitude,* and it turns out that their understanding of magnitude is logarithmic. That is, their understanding of magnitude gets worse as the numbers get bigger. He then goes and looks at studies of children. And by a further series of (very clever) experiments, he establishes that before we enter school, our understanding of numbers is also logarithmic. But by the end of our second year of school, our understanding of magnitude has flattened into an additive process.
*Which is, after all, the most basic need for numbers: to measure magnitude.

The problem is the next step: moving towrd an exponential view of the universe. After all, that’s the organic nature of the game. Bunnies beget bunnies which in turn beget more bunnies. That process is far beyond addition.

Let me put this another way: you know the question about placing a 1mm thick coin on one corner of the chessboard, and doubling it on each subsequent square, and asking how high the pile of pennies would be on square 64? That 184 trillion kilometre answer shouldn’t be so surprising: that answer should be intuitive. The exponential growth of coins echoes the exponential natural process of procreation.

As should the answer to this question: “on what square was the pile of coins half as high as the pile on square 64?” For most of us, the tip-of-the-tongue answer is somewhere around square 32. The intuitive (and correct) answer should be “63” (because the pile doubles on square 64).


Summary: our current mindset places the growth of coins onto a flat arithmetic line, where an exponential mind would see a curve.

What this means from an Investment Standpoint

To put this in terms of an example (and it’s unrealistic because I’m going to use some fairly high returns, but I’m really just trying to show the bias):

  • I say to myself: “Kiddo, it’s time you saved for your retirement.”
  • “You’re only 30. No need for big sacrifices – just take R300 from this month, and put it into this investment earning an annual 12.2% real return. Pretend you lost it, and that you’ll only find it again when you’re 70.”
  • When you look at this scenario, and decide whether it’s a good deal off hand, maybe you’ll say something like “Well that’s about 40 years of investment. 12.2% is close to 10%. 10% a year is 30 bucks. So 30 bucks for 40 years, plus the original R300, maybe the investment will be worth around R1,500 bucks at the low end. But time value of money, so let me go crazy and say it’ll be worth R10,000!! Wait – that really does sound crazy. R3000?
  • Yes – you may know about time value of money – but your estimate is still quite wrong. And that’s where this gut problem comes in – because a preconditioned reliance on arithmetic limits it.
  • In reality, my R300 at that return would be worth R30,000 when I turn 70.

The point of this post: you really should start putting some money aside. Even if it seems only a token amount (like the cost of a couple of meals out per month), it’ll keep busily growing.

And the impact will be so much greater than your mathematical mind can contemplate.

A caveat though: just remember that this also works in reverse, and we often underestimate the impact that even a small amount of inflation can have. As I spoke about here: Compound Interest: How Teens Can Become Millionaires. Or Not.

Rolling Alpha posts opinions on finance, economics, and the corporate life in general. Follow me on Twitter @RollingAlpha, and on Facebook at