What is compound interest
Compound interest is the mechanism by which interest earned in one period is added to the principal, generating further interest in subsequent periods. Simply put: you earn interest on your interest. Einstein reportedly called it "the eighth wonder of the world".
Unlike simple interest (where interest is always calculated on the initial principal), compound interest produces exponential growth over time, most visible over long horizons such as decades.
The formula
Final amount = Principal × (1 + r/n)^(n×t), where r is the annual rate, n is the number of compounding periods per year (1=annual, 12=monthly, 365=daily) and t is the time in years.
Example: €10,000 invested at 7% annual rate for 30 years with annual compounding becomes 10,000 × (1.07)^30 = €76,123. The same investment with simple interest would have produced only €31,000.
Compounding frequency matters
The more frequent the compounding, the larger the final amount:
- Annual: €10,000 at 7% for 30 years → €76,123
- Monthly: €10,000 at 7% for 30 years → €81,165
- Daily: €10,000 at 7% for 30 years → €81,752
The Rule of 72
A quick rule of thumb to estimate the time to double your capital: Years to double ≈ 72 ÷ annual rate (%). At 6% the capital doubles in about 12 years. At 9% in about 8 years.
How to use it in practice
The most powerful variable in compound interest is time, not the rate. Starting to invest €100 per month at 25 produces much more than starting to invest €200 per month at 45, even with the same return. The main instruments are: index funds (ETFs), pension funds, and fixed-term savings accounts.
Compound interest also works in reverse with debts: an unpaid debt accumulates interest on previous interest, exponentially increasing the total debt — the reason why consumer loans with minimum payments can become a financial trap.