Compound Interest

The mathematical force behind every long-term fortune. Model principal, periodic contributions, and compounding frequency.

How the math works.

FV = P(1+r)ⁿ + PMT × ((1+r)ⁿ - 1) / r Where: P = initial principal r = rate per period (annual rate ÷ compounding frequency) n = total periods (years × frequency) PMT = periodic contribution Total Contributed = P + (PMT × n) Interest Earned = FV - Total Contributed

Compound interest is the mathematical foundation of long-term wealth. Each period, your earned interest is added to the principal, and the next period's interest is calculated on that larger amount. The effect is exponential growth — slow at first, then accelerating dramatically.

The formula has two parts: the growth of your initial principal, and the growth of your periodic contributions. The contribution formula is called the "future value of an annuity" and assumes you contribute at the end of each period.

Compounding frequency matters. Monthly compounding (12×/year) yields slightly more than annual compounding at the same nominal rate, because interest begins earning interest sooner. Over 30 years, the difference between annual and monthly compounding at 7% on $10,000 is roughly $3,800.

The most important variable is time. $10,000 at 7% for 30 years becomes $76,123. The same $10,000 at 7% for 40 years becomes $149,745 — nearly double, for the same rate and no additional contributions.