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📈 Foundations

Compound interest

Returns that earn returns — how time turns a rate into an exponential path, and what still breaks the fairy tale.

Compound interest is the mechanism by which a balance grows when returns are left invested so later growth acts on a larger base.

Compound interest sits in the foundations family of this atlas: mechanisms first, products second, hype never.

Use the calculator for scenarios, then return to the section pages when you want the vocabulary behind the curve.

Core ideaInterest on interest
Classic formA(1+r)^n
HorizonMulti-year
EnemyFees & taxes
AllyReinvestment
ToneEducational

Profile

Time sensitivity
96
Rate sensitivity
88
Contribution leverage
72
Behaviour risk
55
Tax & fee drag
70
Horizon fit
90

Seven chapters

The idea

Compound interest is the mechanism by which a balance grows when returns are left invested so later growth acts on a larger base.

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The math

Formulas, worked examples and rules of thumb for compound interest, with inflation and fees kept in view.

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Levers

What you can actually pull when thinking about compound interest: contributions, time, costs, behaviour and wrappers.

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History

A short history of ideas and institutions behind compound interest.

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Pitfalls

Common traps and myths around compound interest, with practical fixes.

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Practice

A practical sequence for applying compound interest without turning life into a spreadsheet cult.

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Today

Modern context for compound interest: rates regimes, apps, FIRE debates and longevity.

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Frequently asked questions

What is compound interest in one sentence?
Compound interest is the mechanism by which a balance grows when returns are left invested so later growth acts on a larger base.
Is this financial advice?
No. Tool-Lifes pages are educational atlases. Decisions need your goals, constraints and, when appropriate, a licensed adviser.
Do I need a high return for compounding to matter?
Higher net rates help, but time and contributions often dominate — especially early. Costs and behaviour can erase a “good” rate.
How should I use the calculator?
Treat outputs as scenario sketches. Vary contribution, rate, fees and inflation to see which lever moves your goal date.
What about inflation?
Always ask whether a figure is nominal or real. A high nominal path can still lose purchasing power.
Are past returns a promise?
No. Illustrations use round teaching numbers. Markets, inflation and taxes change.
Where do fees show up?
In the net rate that compounds. Expense ratios, advice charges and spreads all reduce terminal wealth.
What page should I read next?
From foundations, continue to contributions-vs-rate or fee-drag; for behaviour, open consistency-habit or panic-selling.

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