Compounding: why your brain cannot feel it
Your brain does straight lines. Money does curves. That gap is where most of the wealth is.
4 min read
Every other lesson here is only worth reading because of this one. Compounding (returns earning their own returns) is what turns ordinary amounts into serious ones, and human intuition is genuinely terrible at it.
First, a guess
| Day | Value |
|---|---|
| 1 | $0.01 |
| 10 | $5.12 |
| 15 | $163.84 |
| 20 | $5,242.88 |
| 25 | $167,772.16 |
| 28 | $1,342,177.28 |
| 30 | $5,368,709.12 |
Look at where the money actually appears. At day 20, after two thirds of the time has elapsed, you have $5,242. More than 99.9% of the final amount arrives in the last third. On day 29 you are at $2.68 million, and a single day later you have gained another $2.68 million.
That is the shape of the thing. Almost nothing happens, for a long time, and then an enormous amount happens quickly. Anyone who quits during the flat part concludes it does not work, and they quit while being entirely right about what they had observed so far.
The realistic version
Doubling daily is not available. A 10% annual return roughly is, over long periods, in broad share markets. Here is someone investing $12,000 a year at 10%:
| After | Total contributed | Balance | Profit (never contributed) |
|---|---|---|---|
| 5 years | $60,000 | $80,587 | $20,587 |
| 10 years | $120,000 | $210,374 | $90,374 |
| 15 years | $180,000 | $419,397 | $239,397 |
| 20 years | $240,000 | $756,030 | $516,030 |
| 30 years | $360,000 | $2,171,321 | $1,811,321 |
Read the last column. At five years, most of the balance is money they put there. At thirty years, 83% of it is profit: it was never contributed by anyone. It was produced by the money that was already in the account.
The shape is worth holding onto. Their contributions go in as a straight line, the same amount every year. Their balance does not move in a straight line at all: it tracks the contributions closely for the first several years, then separates, and the gap keeps widening for as long as they leave it alone. Everything in that gap is money nobody put in.
Why this is hard to feel
Human intuition is linear. We are good at estimating things that add and bad at estimating things that are exponential. When you imagine your balance in 20 years, your brain quietly performs addition: this much a year, times twenty. That estimate is not slightly low, it is wrong by a factor of several.
The practical consequence is a predictable mistake. The early years feel pointless, because they genuinely do look pointless. So people delay, and delay is the one thing compounding cannot forgive, because the years you remove are the ones that would have been doing the most work at the end.
Check yourself
2 questions on this lesson. Nothing is recorded or sent anywhere.
1In the doubling-cent example, roughly how much of the final $5.37 million exists at day 20?
More than 99.9% of the total arrives in the final third of the period. That is why quitting early feels justified and is catastrophic.
2After 30 years of investing $12,000 a year at 10%, roughly how much of the $2.17 million was actually contributed?
Contributions are a straight line. The balance is a curve. The gap between them is the whole point.