If Money School could teach only one lesson, it would be this one. Compounding is the engine under everything else — savings, pensions, debt, investing — and once you truly see it, several money decisions make themselves.
Simple vs compound: the £100 example
Put £100 somewhere earning 5% a year. Simple interest would pay you £5 every year, forever — £5, £5, £5. Compound interest pays £5 the first year, then 5% of £105 the next (£5.25), then 5% of £110.25 — the interest starts earning interest. In year one the difference is pennies and looks laughably unimportant. That's the trap: compounding is invisible at the start and unstoppable at the end. Left thirty years, that £100 becomes £432 — and £332 of it is growth you never lifted a finger for.
Two acronyms, decoded once and for all
AER (Annual Equivalent Rate) is the honest yardstick for savings: what you'd actually earn over a year with compounding included, letting you compare any two accounts fairly whatever their small print.
APR (Annual Percentage Rate) is the same idea pointed at borrowing: the true yearly cost of credit including standard fees. One number, two directions — AER is compounding working for you, APR is compounding working for the other side. That's the entire secret of the finance industry in one sentence, and it's why the same maths that builds a pension can bury a credit card holder. We'll meet APR's dark side properly in lesson three.
Why time beats amount (the bit that changes behaviour)
Because growth accelerates, pounds saved early do vastly more work than pounds saved late. Someone putting away £50 a month at 5% for 40 years ends up with more than double the result of the same £50 started 10 years later — not double the missed contributions, double-ish the outcome. The early pounds aren't slightly better; they're the MVPs of the whole squad. This is why the standard advice to young savers isn't "save a lot", it's "start anything, now".
The rule of 72 (party trick, genuinely useful)
Divide 72 by a growth rate and you get roughly how many years money takes to double. At 4%, about 18 years; at 6%, about 12. It works in reverse for prices too: at 3% inflation, the buying power of cash under the mattress halves in about 24 years — which is the polite way of saying that "not deciding" what to do with long-term money is itself a decision, with a cost.