Compound Interest
Compound interest is growth applied to growth --- the force that turns small, consistent contributions into transformative wealth over time. It is back-loaded, counterintuitive, and the most patient force in finance.
What is it?
Simple interest earns a return on the original amount only. Compound interest earns a return on the original amount plus all previously accumulated returns. The difference is the difference between linear and exponential growth.1
CHF 10,000 at 7% simple interest earns CHF 700/year, every year: CHF 17,000 after 10 years. CHF 10,000 at 7% compound interest earns CHF 700 in year one, CHF 749 in year two (7% of CHF 10,700), CHF 801 in year three, and so on: CHF 19,672 after 10 years. After 30 years the gap is dramatic: CHF 31,000 (simple) vs CHF 76,123 (compound).
The key insight from time-value-of-money is that money has a time dimension. Compound interest is what happens when that time dimension runs long enough for growth-on-growth to dominate the original contribution.
Warren Buffett’s fortune illustrates the extreme case. Of his approximately USD 130 billion net worth, over 99% was accumulated after his 50th birthday --- not because he became a better investor, but because the compounding base had grown large enough that each year’s percentage return produced enormous absolute growth.2
In plain terms
A snowball rolling downhill. It starts small. Each rotation picks up more snow. The more snow it has, the more it picks up per rotation. After enough hill, the snowball is bigger than you ever expected from the tiny ball you started with.
At a glance
The compounding curve (click to expand)
graph LR Y0["Year 0<br/>CHF 10K"] --> Y10["Year 10<br/>CHF 20K"] Y10 --> Y20["Year 20<br/>CHF 39K"] Y20 --> Y30["Year 30<br/>CHF 76K"] Y30 --> Y40["Year 40<br/>CHF 150K"] style Y0 fill:#bdc3c7,color:#2c3e50 style Y10 fill:#95a5a6,color:#fff style Y20 fill:#7f8c8d,color:#fff style Y30 fill:#2c3e50,color:#fff style Y40 fill:#27ae60,color:#fffKey: At 7%, money roughly doubles every 10 years (Rule of 72: 72/7 ≈ 10.3). More than half the total growth happens in the final decade. Compounding is back-loaded --- patience is not optional.
How does it work?
1. The Rule of 72
A quick mental shortcut: divide 72 by the annual return rate to get the approximate doubling time.
| Rate | Doubling time |
|---|---|
| 4% | ~18 years |
| 6% | ~12 years |
| 8% | ~9 years |
| 10% | ~7.2 years |
| 12% | ~6 years |
At 7%, your money doubles in ~10 years, quadruples in ~20, and reaches 8x in ~30. The acceleration comes from each doubling applying to a larger base.
2. The cost of delay
Because compounding is back-loaded, the early years feel pointless --- your CHF 10,000 becomes CHF 11,000. Not life-changing. The temptation is to wait until you have “real money” to invest. This is the most expensive mistake in personal finance.
If you invest CHF 200/month starting at 25, at 7% you will have approximately CHF 525,000 by age 60. If you start at 30 --- just five years later --- you will have approximately CHF 365,000. Five years of delay costs CHF 160,000. Not because you saved CHF 12,000 less, but because those CHF 12,000 missed 30 years of compounding.
Starting imperfect now always beats starting optimal later.
3. Compounding beyond money
The same mathematical structure applies to anything that accumulates and builds on itself:
- Skills compound: each new capability makes learning the next one easier
- Reputation compounds: each delivered project makes the next client easier to find
- Relationships compound: each connection opens doors to more connections
- Knowledge compounds: each concept understood makes the next concept more accessible (this is literally what your knowledge architecture does)
Your vault --- 144 concept cards, 23 learning paths, prerequisite chains --- is a compounding system. Each card makes the next one richer because it connects to an existing network. The value of the 145th card is greater than the value of the 1st because it has 144 nodes to connect to.
Why do we use it?
Key reasons
1. Motivation to start. Understanding that early contributions matter disproportionately because they compound the longest overcomes the inertia of “I don’t have enough to make a difference.” 2. Patience. The curve looks flat for years before it curves upward. Knowing this prevents you from quitting during the boring middle. 3. Decision framework. Every spending vs investing decision is implicitly a compounding question: “What would this franc become in 20 years?”
Check your understanding
Five questions (click to expand)
- Calculate the difference between CHF 10,000 at 7% simple vs compound interest over 30 years. Why is the gap so large?
- Use the Rule of 72 to estimate how long it takes CHF 5,000 to become CHF 40,000 at 8% annual return.
- Explain why starting to invest at 25 vs 30 produces a disproportionate difference at 60, even though the contribution difference is only 5 years.
- Apply the compounding concept to a non-financial domain. How does your knowledge architecture compound?
- Argue for or against: “The single best financial decision a 30-year-old can make is to start investing anything, no matter how small, immediately.” Use compounding math.
Where this concept fits
Where this concept fits
graph TD TVM[Time Value of Money] --> CI[Compound Interest] CI --> FI[Financial Independence] CI --> RR[Risk and Return] SR[Savings Rate] --> CI style CI fill:#4a9ede,color:#fff
- Prerequisites: time-value-of-money
- Leads to: financial-independence, risk-and-return