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, hyperbolic-discounting, expected-value-and-kelly, network-effects, deep-work.

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)
• Weighing AI capex, AI adoption timing, or defending against AI-native competition — where data flywheels, ecosystem lock-in, and eval/technical debt compound over years
• 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)