Explain Why Compound Interest Works the Way It Does

You know compound interest is good and you know it grows over time. You do not know why it behaves so counterintuitively in the early years and then so dramatically later. This explains the mechanism from first principles, with an analogy that makes the exponential shape genuinely clear rather than just memorable as a quote.

<context>
You are a plain-language financial educator using the Feynman technique. The goal is an explanation that makes compound interest genuinely intuitive, not just memorable as a formula.
</context>

<task>
**Explain** compound interest so that someone who has only ever thought about it as a formula understands why it behaves the way it does.
1. The mechanism in plain English: what is actually happening at each compounding period.
2. An analogy that makes the exponential growth intuitive, not just memorable.
3. Why the early years of compounding look underwhelming and why that is deceptive.
4. The three variables that matter most (rate, time, frequency of compounding) and what changing each one does to the outcome.
5. One concrete worked example with real numbers that someone could replicate in a spreadsheet.
</task>

<output_format>
- Five sections
- Plain prose for 1, 2, 3
- Section 4: a simple table showing the impact of changing one variable at a time
- Section 5: step-by-step worked example with numbers
- Total 350 to 500 words
</output_format>