Draw a straight line across a piece of paper. That's how most of us picture money growing: a bit more each year, a little progress, the line creeping steadily upward. Completely reasonable. Completely wrong.
Compound interest doesn't draw a straight line. It draws something that looks flat for an embarrassingly long time, then suddenly goes nearly vertical. Economists call this a hockey stick curve. The name makes it sound like a quirk of presentation, a choice of scale, something you could flatten out if you tilted the chart. You can't. That shape is the actual geometry of what's happening. Once you understand the mechanism behind it, it stops looking like an abstraction and starts looking almost alive.
How long before compound interest becomes noticeable?
Simple interest is arithmetic: you put in £1,000, it earns 5%, you get £50. Next year, another £50. Same sum, every year, regular as a bus. Compound interest is different. In year one you still earn £50, but in year two you earn 5% of £1,050 – small change. In year ten you're earning 5% of £1,629. In year thirty, 5% of £4,321. The percentage never changes. The number it's eating through does.
This is what makes it behave less like arithmetic and more like erosion or crystal growth – processes where the size of the thing doing the work keeps increasing, so the effect keeps accelerating. The Grand Canyon didn't get a little wider every year by the same amount. The water kept finding more surface. Compound interest is the same mechanism, pointed at your savings account.
The Optical Illusion in the Numbers
Our brains are genuinely bad at this, and not through any fault of our own. We evolved to track things that grow in straight lines – herds, harvests, distances. Exponential growth isn't something we encounter in ordinary life until we do, and then it's usually bad news: a spreading fire, a debt that got away from us. We look at a compound interest chart and spend most of our time staring at the flat bit at the start, waiting for something to happen. Nothing much does, for ages. And then it does, and it doesn't stop.
The famous illustration is a pond with a single lily pad that doubles in size every day, covering the whole pond in thirty days. On day twenty-nine, it covers half the pond. On day twenty-eight, a quarter. For most of the month, it looks like nothing much. Which is, of course, when the interesting thing is actually happening.
Why the Start of the Curve Is Doing All the Work
The flat early part of a compound curve isn't the boring bit – it's the bit that makes everything else possible. Each quiet year is silently fattening the base, and without those unremarkable early years, there's no big number for the later percentages to land on. This is why people who understand compound interest tend to get slightly evangelical about starting early, even with tiny amounts. A £50 monthly deposit in your twenties will, at a modest rate, genuinely outperform a much larger deposit that began in your forties. Not because of different rates or clever choices, but because the base had longer to grow.
The monstrous thing about compound interest isn't the percentage. It's the patience.
Questions this raises
- What is the rule of 72?
- Does monthly compounding beat annual compounding by much?
- Why do UK savings accounts quote an AER?
