Compound interest is interest earning interest. That single recursive trick is the engine behind every pension, every ISA projection and every "start investing young" lecture — and the maths is more dramatic than most people expect.
Simple vs Compound
£10,000 at 7% simple interest earns £700 every year — £24,500 total after 35 years. Compounded, the same money becomes £106,766. The difference is not the rate; it is that each year of growth joins the capital and grows itself.
The Rule of 72
Divide 72 by your annual return to get the doubling time. At 4%, money doubles every 18 years; at 7%, every 10.3 years; at 10%, every 7.2. Over a 40-year working life, 7% means four doublings — ×16 before contributions.
Why Starting Early Beats Saving More
£200/month from age 25 to 65 at 7% builds ~£480,000. Waiting until 35 and saving £300/month — more money in — reaches only ~£340,000. The first decade of contributions gets 40 years of doubling; nothing later can replace them.
The Dark Side
The same maths powers credit card debt. £3,000 at 24.9% APR compounds against you with a doubling time under 3 years — which is why minimum payments can take decades to clear a balance.