How Compound Interest Actually Works
Compounding is the one piece of financial maths worth understanding properly. Here is the mechanism, the shortcut for estimating it, and the two mistakes that quietly cancel it out.
Compounding gets described so often as “interest on interest” that the phrase stops meaning anything. So let’s take it apart.
The mechanism
Put £10,000 into an account paying 7% a year. After one year you have £10,700. The second year, the 7% applies to £10,700 — not £10,000. You earn £749, not £700.
That extra £49 is the whole idea. It looks trivial. It isn’t, because it repeats.
| Year | Balance | Interest earned that year |
|---|---|---|
| 0 | £10,000 | — |
| 1 | £10,700 | £700 |
| 5 | £14,026 | £918 |
| 10 | £19,672 | £1,287 |
| 20 | £38,697 | £2,532 |
| 30 | £76,123 | £4,981 |
By year 30 the account is earning almost £5,000 a year — half the original deposit — without anyone adding a penny.
The shortcut: the rule of 72
Divide 72 by the annual return to get the number of years it takes to double.
- 7% → about 10.3 years
- 5% → about 14.4 years
- 10% → about 7.2 years
It’s an approximation, and it drifts at high rates, but it’s accurate enough to sanity-check any projection someone shows you. If a pitch claims your money doubles in five years, that implies roughly 14% a year, every year — which should make you ask harder questions.
Why time beats contribution size
Two people, both earning 7% a year:
- Early: invests £5,000 a year from age 25 to 35, then stops. Total contributed: £50,000.
- Late: invests £5,000 a year from age 35 to 65. Total contributed: £150,000.
At 65, Early ends up with more.
Early’s pot compounds for 40 years; Late’s has only 30, and the last decade of Early’s growth happens on a much larger base. This is why “I’ll start when I earn more” is the single most expensive sentence in personal finance.
The two things that cancel it
Fees. A 2% annual fee doesn’t cost you 2%. It costs you 2% of a number that would otherwise be compounding. Over 30 years, a 2% fee can consume roughly half the final balance compared with a 0.2% fee. The fee is charged on the balance, so it compounds too — just against you.
Inflation. A 7% return with 3% inflation is a 4% real return. Compounding nominal numbers and calling it wealth is a common way to feel richer than you are.
What compounding does not do
It doesn’t rescue a bad starting position. It doesn’t work on money you withdraw. And it doesn’t apply to debt in your favour — the same mechanism runs in reverse on a credit card balance, which is why 20%+ APR debt is an emergency, not a budgeting inconvenience.
The maths is neutral. Which direction it runs depends entirely on whether you’re the one charging or the one paying.