compound-interestlisted

# Compound Interest ## Overview Compound interest: a quantity grows at a rate proportional to its current size — growth itself grows — producing exponential accumulation. Formula: A = P × (1 + r)^t. Humans underestimate long-horizon outcomes because cognition extrapolates linearly. Two consequences: **Rule of 72** (doubles in ≈ 72/r periods); **late-period dominance** (most final value comes from the last few periods). Composes with [`lindy-effect`](../lindy-effect/SKILL.md), [`hyperbolic-discounting`](../hyperbolic-discounting/SKILL.md), [`expected-value-and-kelly`](../expected-value-and-kelly/SKILL.md), [`network-effects`](../network-effects/SKILL.md), [`deep-work`](../deep-work/SKILL.md). ## When to Use - Evaluating any long-horizon investment, savings, or wealth decision - Deciding between starting earlier vs. starting later; intensity vs. duration paths - Evaluating compound advantages in business (data, brand, switching cost) - Skill-development planning; recognizing compound decay (fees, atrophy, trust erosion) **Not when:** horizon is short; rate is so low linear approximation is fine; process is genuinely linear; situation requires immediate one-shot intensity. ## Coaching Novices (Adaptive Front Door) - **Engine mode:** user has a concrete long-horizon case → run The Process directly. - **Coach mode:** user is unfamiliar → guide step by step. In Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.