Explain How Compound Interest Actually Works

Compound interest gets cited constantly as a reason to start investing early, and most explanations jump straight to an astonishing end number without explaining what is actually happening. This covers the mechanism, why time matters more than rate in early decades, the rule of 72 as a quick mental tool, how the same mechanism works in debt, and what most people underestimate once they actually understand it.

Explain compound interest in plain English, in a way that makes the actual mechanism clear rather than just presenting a dramatic final number.

Cover:
1. The mechanism: what compound interest is and how it differs from simple interest, using one worked example with the same principal, rate, and period
2. The time variable: why the number of years matters more than the interest rate in the early decades, with a second example showing the same rate over 10 years versus 30 years
3. The rule of 72: what it is and how to use it for a quick mental estimate of doubling time
4. The same mechanism working against you: how compound interest works in debt (credit cards, loans) using a realistic example with typical UK rates
5. The one thing most people underestimate about compound interest: not the end number, but the implication for when to start

All examples should use realistic UK-relevant numbers (ISA rates, credit card APR).