What is compound interest?
With simple interest, you earn the same amount each year on your initial capital. With compound interest, the year's interest is added to the capital, and the following year you earn interest on a larger base.
The difference looks minor at first. It becomes enormous over the long term.
Simple interest: 10,000 + (10,000 × 10% × 20) = €30,000
Compound interest: 10,000 × (1.10)^20 = €67,275
The gap is €37,275 — more than the initial capital itself. That is purely the effect of compounding.
The formula
C = C₀ × (1 + r)ⁿ
Where C₀ is the initial capital, r the annual rate and n the number of years. With regular monthly contributions v:
C = C₀ × (1 + r)ⁿ + v × [(1 + r/12)^(12n) − 1] / (r/12)
The rule of 72
The rule of 72 is the most useful mental tool for reasoning about compound interest:
Comparison: the impact of the rate over 30 years
For €10,000 invested today, with no further contributions:
| Rate | 10 years | 20 years | 30 years | Doubling | Equivalent to |
|---|---|---|---|---|---|
| 3% | €13,439 | €18,061 | €24,273 | 24 years | Savings account |
| 5% | €16,289 | €26,533 | €43,219 | 14 years | Solid bond fund |
| 8% | €21,589 | €46,610 | €100,627 | 9 years | Global ETF |
| 10% | €25,937 | €67,275 | €174,494 | 7.2 years | Selective stock picking |
| 15% | €40,456 | €163,665 | €662,118 | 4.8 years | High-performing small caps |
Compound interest calculator
The effect of time: starting early vs starting late
The most important rule of compound interest: time is the most powerful variable, ahead of the rate and the amount invested.
Example at 9% annualised, €200/month:
- Start at 25 → capital at 65: ≈ €864,000
- Start at 35 → capital at 65: ≈ €337,000
- Start at 45 → capital at 65: ≈ €124,000
Ten years' delay between ages 25 and 35 costs €527,000. Yet 10 years × 12 months × €200 = only €24,000 of extra contributions. It is the compound interest on those first 30 years that creates the gap.
Two behaviours break the compounding effect: 1) withdrawing the capital before maturity (exponential growth happens mostly in the final years), 2) paying too much in fees (an extra 0.5% of fees per year over 30 years reduces the final capital by 14%). On ETFs, management fees are the most controllable factor.
A well-selected small-cap portfolio at 12% annualised vs an ETF at 8%: over 25 years, the gap is ×2 on the final capital.