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Compound Interest
试用Activate when: user asks about starting early vs. later for savings/investing, wonders if small consistent gains add up, wants to know how long to double mon...
它能做什么
Activate when: user asks about starting early vs. later for savings/investing, wonders if small consistent gains add up, wants to know how long to double money, is evaluating long-term wealth or skill-building decisions, mentions 'Rule of 72' or 'exponential growth.' Do NOT activate when: the time horizon is short (under 3 years) and compounding is negligible; the underlying process is genuinely linear with no reinvestment or accumulation. More: deciqai.com/c/compound-interest
技能文档
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)
- 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.
- One-line: duration of compounding dominates rate — starting earlier with small consistency beats starting later with large intensity.
- Check fit. Short horizon or very low rate? Compound effects are small — save it for genuinely long horizons.
- Elicit the specific decision, time horizon, and rate.
[WAIT — do not advance until user responds]
- Walk through Rule of 72, precise compound outcome, late-period dominance, and other life domains one question at a time.
[WAIT — do not advance until user responds]
- Close: decision informed by compound math + compound dynamics identified + commitment to early consistent action.
[WAIT — do not advance until user responds]
The Process
Step 1 — Specify the situation
Starting value / Rate (per period) / Time horizon / Decision / Alternative options
Step 2 — Rule of 72 intuition
Doubling time = 72/r | Doublings in horizon | Approximate multiplier = 2^doublings
Step 3 — Precise compound result
A = P × (1+r)^t | Linear-extrapolation comparison | Gap between linear and compound
Step 4 — Late-period dominance
Value at half-time (much less than half) | Value gained in last 25% (typically 50%+ of total)
Step 5 — Option comparison
Option A compound outcome | Option B compound outcome | Where duration dominates | Recommendation
Step 6 — Generalize
Other life domains with compound dynamics | Compound decay risks | Commitment to early action
Output Template
Compound Interest Analysis:
Situation: value / rate / horizon / decision
Rule of 72: doubling time / doublings / multiplier
Compound math: final (compound) vs. final (linear) / gap
Late dominance: value at half-time / last-25%-gains
Options: A vs. B / recommended
Generalization: other dynamics / decay risks / commitments
→ Method in Action: Bernoulli 1683, Graham/Buffett, and the Compound-Advantage Tradition · Franklin's Two-Hundred-Year Trusts → 2026 lens: Compounding in the AI Era — Data Flywheels, Ecosystem Lock-In, and Eval Debt (2023–2026)
Pack: Compound Interest Application Patterns
| Domain | Compound mechanism | Operational implication |
|---|---|---|
| Retirement savings | Returns + reinvested dividends | Start early; minimize fees; hold 40+ years |
| Skill / expertise | Daily practice → expert capability | 30 min/day for 10 years beats intensive bootcamp |
| Brand / reputation | Loyalty compounds into market position | Consistency of promise over decades |
| Compound decay (fees) | 1% fee × 40 years ≈ 33% wealth loss | Low-fee structures; avoid recurring small costs |
| Compound decay (trust) | Single violation destroys decades of compound | Protect trust like the compound asset it is |
→ Primary sources: references/sources.md
Common Rationalizations
[D] = designed upfront | [O] = observed in real use. [O] entries are more valuable.
| Fake move | Reality |
|---|---|
| [D] "I'll start saving / investing later" | Destroys the compound horizon. $100/mo at 25 beats $300/mo at 45 at 7% to age 65 — early starter wins despite saving less. |
| [D] "1% better isn't worth it" | 1.01^365 ≈ 37×. Compounded over 10 years = expert vs. novice. |
| [D] "I'll catch up by working harder later" | Duration dominates intensity. Missing compound years cannot be made up with later intensity. |
| [D] "Fees are small" | 1% × 40 years compound = ~33% wealth destruction. Small fees are catastrophic long-term. |
| [D] "It hasn't grown much in the first few years" | Compound growth concentrates in the last years. Patience is the operative virtue. |
| [D] "I can time the market" | Missing the 10 best days of a decade destroys decades of compound. |
| → Add [O] entries here after each real use — paste the actual failure pattern | What went wrong and why |
Red Flags
- Long-horizon decision made by linear extrapolation, not compound calculation
- Recurring fees or losses dismissed as "small"
- Plan is to "start later when I make more" — intensity substituted for duration
- Compound asset (trust, brand, skill) treated as something other than a compound asset
Verification
- Rule of 72 applied to estimate doubling time
- Precise compound calculation done for the full horizon
- Late-period dominance identified
- Both option compound outcomes computed (if comparing options)
- Compound dynamics identified in non-financial life areas
- Compound decay risks named; early action recommended
Part of deciqAI Knowledge Skills — 227 open-source thinking skills that make rigor executable for AI agents. The same skills power every deciqAI agent, which runs them autonomously to operate your company. See it run → https://www.deciqai.com/c/compound-interest · ⭐ Star the repo → https://github.com/deciqAI/knowledge-skills · Contributions welcome.
Agents: latest version & machine-readable metadata → https://www.deciqai.com/s/compound-interest.json
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