What Is the Compound Interest Effect?
Compound interest is the most powerful tool for long-term wealth accumulation – Albert Einstein famously called it the "eighth wonder of the world". The principle is simple: you earn interest not only on your initial capital, but also interest on the interest you have already received. Over time, this causes your wealth to grow exponentially rather than linearly.
For detailed calculations, you can use our free compound interest calculator.
In this guide, we explain the mathematical formula behind compound interest, demonstrate its massive impact over different timeframes, and introduce the handy "Rule of 72". We also look at inflation, the often-forgotten factor in wealth planning.
What Is the Mathematical Formula for Compound Interest?
The basic formula for compound interest on a one-time investment (Einmalanlage) is:
Future Value = Initial Capital × (1 + Interest Rate)Number of Years
Or: Kn = K0 × (1 + r)n
- Kn: End capital after n years
- K0: Starting capital
- r: Annual interest rate (e.g., 0.07 for 7%)
- n: Investment period in years
Example: You invest 10,000 € with an annual return of 7%. After 30 years: 10.000 × (1.07)30 = 76,123 €. Your capital has multiplied more than 7.6 times, purely through compounding!
Growth Comparison: One-Time Investment vs. Monthly Savings Plan
The following table shows the compound interest effect at a **7% annual return** (the typical long-term historical average of a globally diversified equity ETF like the MSCI World):
| Scenario | Total Contributions | After 10 Years | After 20 Years | After 30 Years |
|---|---|---|---|---|
| One-Time 10,000 € | 10,000 € | 19,672 € | 38,697 € | 76,123 € |
| Savings Plan 200 €/month | 24k / 48k / 72k € | 34,603 € | 104,186 € | 243,994 € |
| Savings Plan 500 €/month | 60k / 120k / 180k € | 86,509 € | 260,464 € | 609,985 € |
Key Takeaway: If you invest 500 € monthly for 30 years at 7%, you contribute 180,000 € but end up with about 610,000 €. The pure compounding profit is over 430,000 €!
What Is the Rule of 72?
The Rule of 72 is a simple mental shortcut to estimate how many years it takes for your investment to double:
Years to Double ≈ 72 ÷ Annual Return (%)
- At a 7% return, your money doubles in about 10.3 years.
- At a 10% return, your money doubles in about 7.2 years.
Why Is Starting Early Critical?
Compound interest needs time. For instance:
- Investor A starts at age 25, saving 200 €/month for 10 years (until 35), then stops contributing but leaves the money to compound until 65. Total contributed: 24,000 €. Ending wealth at 7%: ca. 267,000 €.
- Investor B starts at 35, saving 200 €/month for 30 years (until 65). Total contributed: 72,000 €. Ending wealth at 7%: ca. 244,000 €.
Investor A contributed three times less capital, yet ends up with more money! This is the power of starting early.
The Role of Inflation
Inflation erodes purchase power. At 2% annual inflation, 100 € today has the purchase power of only 55 € in 30 years. To find real growth, always calculate with the real return (Nominal Return − Inflation Rate).
Sources: Financial mathematics standards, historical MSCI World Index returns (approx. 7% nominal p.a. since 1975), Deutsche Bundesbank inflation stats.