The Power of Compound Interest
Compound interest is the process by which interest earned on a sum of money is reinvested, so that in subsequent periods, interest is earned on the original principal plus all previously accumulated interest. This creates exponential growth — the defining feature of long-term wealth accumulation. Irving Fisher formalized the mathematical theory of interest in 1930, building on centuries of practical banking knowledge.
The Formula
The compound interest formula A = P·(1 + r/n)^(nt) captures four key variables: principal (P), annual rate (r), compounding frequency (n), and time (t). Adding regular contributions PMT transforms this into the future value of an annuity: A = P·(1+r/n)^(nt) + PMT·[((1+r/n)^(nt) - 1)/(r/n)]. The exponential nature means small changes in rate or time horizon create dramatic differences in outcomes.
The Rule of 72
A powerful mental shortcut: divide 72 by your annual return percentage to estimate doubling time. At 7% per year, money doubles in about 10.3 years. At 10%, it doubles in 7.2 years. This rule, attributed to Luca Pacioli in 1494, makes it easy to grasp the implications of different return rates. After one doubling, your money is 2x; after two doublings, 4x; after three, 8x — the power of exponentials becomes staggering over decades.
Time vs. Contributions
The visualization reveals a crucial insight: in the early years, your contributions (cyan area) dominate. But over time, the interest earned (red area) overtakes and eventually dwarfs your contributions. This is why starting early is so important — a 25-year-old investing $500/month at 7% will have roughly $1.1 million by 65, of which only $240,000 is contributions. The remaining $860,000 is pure compound growth. Starting at 35 with the same parameters yields only about $500,000. A decade of lost compounding costs more than half the final result.