Compound Interest, Explained With Actual Numbers

Simple versus compound: one line of difference

Simple interest pays only on the original amount. 1,000 euros at 5% simple interest earns 50 euros every year, forever: after 30 years, 1,000 + 30 × 50 = 2,500 euros.

Compound interest pays on the running total. The same 1,000 euros at 5% compounded yearly becomes 1,000 × 1.05³⁰ ≈ 4,322 euros after 30 years. The extra 1,822 euros is interest earned on interest, and it is bigger than all the simple interest combined.

The formula behind every compound calculation is A = P × (1 + r/n)^(n×t): starting amount P, yearly rate r, n compounding periods per year, t years. Monthly compounding (n = 12) at 5% turns the effective yearly rate into about 5.12%; the difference between yearly and monthly compounding is real but small compared to the difference the RATE and the TIME make.

Why the curve feels slow, then absurd

Compounding is an exponential curve, and exponential curves spend most of their length looking flat. In the 4,322-euro example, the first decade earns about 629 euros, the second about 1,024, the third about 1,670. Same rate, same money, but each decade out-earns the previous one, because the base keeps growing.

This is why starting early is the one advantage that cannot be bought back. Saving 200 euros a month at 6% from age 25 to 65 builds roughly 397,000 euros; starting at 35 with the same payments builds roughly 200,000. Ten missing years cost about half the outcome, even though the late starter only paid in 25% less money.

The rule of 72, and its fine print

Divide 72 by the yearly rate to estimate the doubling time. At 6%, money doubles in about 12 years; at 3%, about 24. It works because 72 sits close to the true mathematical constant (about 69.3) while dividing cleanly by 2, 3, 4, 6, 8, 9 and 12.

The rule cuts both ways. Inflation at 3% HALVES your purchasing power every 24 years, and a credit card at 18% doubles a debt in four years if nothing is paid. Compounding does not care which direction it works in.

Fees are compound interest in reverse

A 1.5% yearly fee sounds harmless next to a 7% return. But the fee compounds too: over 30 years, 100,000 euros at 7% grows to about 761,000, while at 5.5% (the same return minus the fee) it grows to about 498,000. The fee consumed a third of the outcome, quietly, one year at a time.

The same logic explains why paying off high-interest debt is usually the best 'investment' available: erasing an 18% debt is a guaranteed, tax-free, risk-free 18% return, a number no honest market offers.

The honest closing note: real markets do not pay a smooth fixed rate; returns vary year to year, and the calculations above describe the mechanism, not a promise. Use them to compare scenarios and understand fees, not as a forecast, and treat anyone selling you a guaranteed high compound return with the suspicion the math itself recommends.