How compound interest actually works

Compounding is slow, then unreasonably fast. Here is what that looks like in real numbers — and the three factors most projections quietly leave out.

Compounding, in one sentence

Compound interest means your returns start earning returns. Simple interest pays only on what you originally deposited; compound interest pays on your deposit plus everything it has already earned. That difference is invisible for the first few years and enormous after twenty.

What it looks like with real numbers

Start with $5,000, add $300 a month, assume a 7% annual return, and leave it for 20 years:

• Total you deposited: $77,000
• Growth earned: $100,383
• Final balance: $177,383

More than half the final balance is money you never put in. Run the same plan for 30 years instead and your contributions rise by roughly half, while growth roughly triples. That non-linearity is the whole point.

The Rule of 72

A shortcut worth memorising: divide 72 by your annual return to estimate the years it takes money to double.

• At 7%: roughly 10 years
• At 10%: roughly 7 years
• At 3%: roughly 24 years

It's approximate, but accurate enough to sanity-check any projection in your head — including one a salesperson shows you.

Why starting early beats contributing more

Because the doubling happens at the end. Money invested in year one gets every doubling period; money invested in year fifteen gets almost none. This is why "invest something now" usually beats "wait until I can invest properly" — the extra years are doing work that a larger contribution later can't replicate.

Three things that quietly shrink the result

Inflation

$177,000 in twenty years won't buy what $177,000 buys today. If you want the answer in today's purchasing power, use a real return — your expected return minus expected inflation. Historically that means modelling something closer to 4–5% rather than 7%.

Fees

A 1% annual fund fee doesn't cost you 1%. It compounds against you across the entire horizon and can consume a fifth or more of your final balance. When comparing funds, subtract the expense ratio from your assumed return before running the numbers.

Sequence of returns

Real markets deliver +20% years and −15% years in unpredictable order. Over long horizons the average tends to smooth out, but a bad run early in retirement — when you're withdrawing rather than adding — matters far more than the average suggests.

What rate should you actually assume?

There's no correct number, and anyone offering one confidently deserves suspicion. As reference points: broad stock indices have historically averaged roughly 7–10% nominal over multi-decade periods; bonds considerably less; savings accounts less again. Past averages are not a promise about your particular time period.

A sensible habit is modelling a conservative case and an optimistic case rather than a single figure, and planning around the conservative one.

Where compounding doesn't apply

For goals inside about five years, cash savings usually beat investing. Compounding needs time, and a market drop right before you need the money is unrecoverable. Compounding is a long-horizon tool — treat it as one.