What compounding actually is

Compounding gets explained with snowballs, which is a metaphor that tells you the answer is "it gets big" without telling you why. Here is the mechanism instead.

Three separate things are growing

Put 1,000 into something that returns 7% a year and leave it alone.

In year one it earns 70. Straightforward. In year two it earns 7% of 1,070, which is 74.90 — the extra 4.90 is the return on last year's return. That 4.90 is the entire idea. Everything else is that same step repeated.

By year twenty the annual gain is around 253, and none of that came from you putting more in. The money earning money is now several layers deep: your original amount, the returns on it, the returns on those returns, and so on.

Why the curve bends late

The unhelpful thing about compounding is that almost nothing appears to happen for a long time. At 7%, money roughly doubles every ten years. So:

• Year 10: about 2× your starting amount
• Year 20: about 4×
• Year 30: about 8×
• Year 40: about 15×

The jump from year 30 to year 40 adds roughly seven times your original amount. The jump from year 0 to year 10 adds one. Same ten years, same rate — the later decade is worth seven times the earlier one, because it is operating on a much larger base.

This is why the first decade feels like nothing is happening and why the arithmetic rewards starting rather than optimising. It also means the tail end is doing most of the work, which cuts both ways: a plan that needs the last decade to arrive is a plan with a lot riding on one decade.

The rule of 72, and why this site does not use it

Divide 72 by the return and you get roughly the years to double: 72 ÷ 7 ≈ 10.3 years. It is a genuinely useful thing to be able to do in your head.

It is also an approximation. The exact figure at 7% is 10.24 years, and the shortcut drifts further as rates get further from about 8%. The calculators here use the exact form, so their answers will occasionally differ slightly from a mental estimate. The mental estimate is the one that is wrong.

It works against you too

Nothing about the mechanism cares which direction it points. A 1% annual fee compounds against your balance with exactly the same relentlessness — which is why a 1% charge costs far more than 1% of your final pot. Inflation does the same thing to cash. Debt at 20% doubles what you owe in under four years.

The reason compounding is discussed almost exclusively as a positive is that it is usually being explained by someone selling something. The mechanism is neutral.

The one honest caveat

Every sentence above assumed a steady 7%. Real returns are not steady, and the smooth curve every calculator draws — including the ones on this site — is a convenience, not a forecast. That is worth its own page.