How does compound interest actually work?

Compound interest is interest earned on interest already earned. Simple interest pays only on the original sum; compound interest pays on the original sum plus everything accumulated so far, so the balance grows on an accelerating curve rather than a straight line.

A concrete comparison. Put £10,000 in at 5% a year. With simple interest you receive £500 every year — £25,000 after 30 years. With annual compounding, year one earns £500, year two earns 5% of £10,500, and so on. After 30 years the balance is about £43,200. Same rate, same deposit, £18,000 difference, produced entirely by the interest earning its own interest.

The two variables that matter most are rate and time, and time matters more than people expect. Because growth is exponential, most of the gain arrives late. In the example above, more is added in the final decade than in the first two combined. This is why starting early has an effect that later contributions struggle to match.

The Rule of 72 is a useful shortcut: divide 72 by the annual rate to approximate how many years a balance takes to double. At 6%, roughly 12 years. At 3%, roughly 24. It is an approximation, but a good one for typical rates.

Compounding frequency matters too — monthly compounding beats annual at the same nominal rate. This is what AER and APY figures express: the effective annual rate once compounding is accounted for, which is why they are the comparable numbers.

It works identically against you on debt. Credit card interest compounds on unpaid balances, which is how a modest balance carried for years grows far beyond what was spent.

Inflation erodes real returns, so nominal growth overstates purchasing power gained.