The Basic Concept
Simple interest grows linearly: you earn interest only on your principal. Compound interest grows exponentially: you earn interest on your principal and on all the interest you have already earned.
The difference, over long periods and at meaningful rates, is staggering.
Example: €10,000 invested for 30 years at 7% annual return.
- Simple interest: €10,000 + (€10,000 × 7% × 30) = €31,000
- Compound interest (annual): €10,000 × (1.07)³⁰ = €76,123
The same money, the same rate, the same time – but compounding produces more than twice the result of simple interest.
The Formula
A = P × (1 + r/n)^(n×t)
Where:
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (as a decimal: 7% = 0.07)
- n = compounding frequency per year (1=annual, 12=monthly, 365=daily)
- t = time in years
Compounding Frequency Matters
More frequent compounding means slightly more growth. However, the difference between monthly and daily compounding is small – the big variable is the rate and the time.
| Compounding | €10,000 at 7% for 30 years |
|---|---|
| Annual | €76,123 |
| Monthly | €81,165 |
| Daily | €81,645 |
The Rule of 72
A simple mental shortcut: divide 72 by the annual interest rate to get the approximate number of years it takes for your money to double.
- 72 ÷ 7% = ~10.3 years to double at 7%
- 72 ÷ 4% = ~18 years to double at 4%
- 72 ÷ 10% = ~7.2 years to double at 10%
Time Is the Most Powerful Variable
Because compound interest is exponential, the most powerful thing you can do is start early. Two examples:
Alex invests €5,000/year from age 25 to 35 (10 years), then stops. Total invested: €50,000. Jordan waits until 35, then invests €5,000/year until age 65 (30 years). Total invested: €150,000.
At 7% annual return, both have the same balance at 65. Alex invested a third of the money but started 10 years earlier. Each decade of delay costs you roughly half your eventual wealth.
Compound Interest Works Against You Too
The same math that builds wealth also builds debt. Credit card debt at 20% APR compounds monthly. If you carry a €3,000 balance and only pay the minimum, the debt can take 15+ years to clear and cost more than the original balance in interest.
This is why financial advice consistently prioritizes paying off high-interest debt before investing – no investment reliably returns 20% per year, so eliminating 20% debt is the better mathematical choice.
Real-World Applications
- Savings accounts (low rates, safe)
- Index funds and ETFs (historically ~7% real return for broad market indices over long periods)
- Pension/retirement accounts (compounding inside tax-advantaged wrappers is especially powerful)
- Mortgages (amortization – you pay more interest early because the outstanding balance is higher)
- Credit card debt (works against you – pay off monthly)
Calculate Compound Growth
The Compound Interest Calculator on this site lets you model different principal amounts, rates, time periods, and compounding frequencies – including regular monthly contributions – entirely in your browser.
Summary
Compound interest earns returns on returns, producing exponential rather than linear growth. Time and rate are its two key inputs. Starting early is more powerful than investing more later. The same mechanism that builds savings destroys borrowers who carry high-interest debt.