Compounding

Compounding applies each period's proportional change to the accumulated base. With constant rate r and no external flows, the result is B₀(1 + r)ⁿ; variable rates require multiplying the period factors.

Compounding occurs when proportional changes apply to the accumulated base. With constant per-period rate r and no added or removed amounts, the base after n periods is B₀(1 + r)ⁿ. With varying rates, multiply the period factors. Additive contributions, withdrawals, fees, and limits require an expanded calculation.

The mechanism matters more than the inspiring metaphor. Knowledge or relationships may benefit from earlier investment, but they do not necessarily follow a constant proportional-growth law. Losses can shrink the base without erasing it, interruptions do not always reset it, and favorable compounding is conditional on returns and retained resources.

When to use it

When choosing between quick wins and sustained investment. When evaluating whether to start something that will pay off slowly. When designing personal development or investment strategies.

How it can help

Specify the base, rates, horizon, costs, and external flows. Compare scenarios using multiplication and distinguish mathematical compounding from analogies about cumulative benefits.