Long term & Saving

Compound interest and the rule of 72: the magic of time in the markets

Albert Einstein is said to have described compound interest as "the eighth wonder of the world". The formula is simple, but its long-term effects are spectacular — and deeply counter-intuitive. This guide explains the mechanism, the rule of 72, and why a 10-year head start can double your final capital at retirement.

📅 May 2026 ⏱ 7 min read 📊 Beginner level

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.

A concrete example: €10,000 at 10% for 20 years
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:

72 ÷ r = years
Annual rate of return
At 9% → doubling in 8.0 years

Comparison: the impact of the rate over 30 years

For €10,000 invested today, with no further contributions:

Rate10 years20 years30 yearsDoublingEquivalent to
3%€13,439€18,061€24,27324 yearsSavings account
5%€16,289€26,533€43,21914 yearsSolid bond fund
8%€21,589€46,610€100,6279 yearsGlobal ETF
10%€25,937€67,275€174,4947.2 yearsSelective stock picking
15%€40,456€163,665€662,1184.8 yearsHigh-performing small caps

Compound interest calculator

🧮 Compound interest calculator
Initial capital (€)
Monthly contribution (€)
Annual rate (%)
Duration (years)
Total capital contributed
Final capital
Gains generated
Gains / contributions ratio
Doubling of the initial capital

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.

The enemies of compound interest
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.
Putting compound interest to work in small caps

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.

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Frequently asked questions

Interest calculated on the initial capital AND on the interest already accumulated. In the stock market, one year's gains are reinvested and themselves generate gains the following year. Over the long term, the effect is exponential.
Divide 72 by the annual rate of return to estimate the number of years needed to double the capital. At 6% → 12 years. At 9% → 8 years. At 12% → 6 years.
C = C₀ × (1 + r)^n, where C₀ is the initial capital, r the annual rate and n the number of years. Example: €10,000 at 10% for 20 years = 10,000 × (1.10)^20 = €67,275.
€10,000 over 30 years: at 3% → €24,273. At 7% → €76,123. At 10% → €174,494. At 15% → €662,118. The difference between 3% and 10% is ×7.
Exponential growth is concentrated in the final years. A 10-year head start at 9% with €200/month represents €527,000 of extra capital at age 65, for only €24,000 of additional contributions. Every year of delay costs proportionally more.

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