E (Compound Interest Definition)

Colorized Definition

\newcommand{\growth}{\color{c1}}
\newcommand{\unitQuantity}{\color{c2}}
\newcommand{\unitInterest}{\color{c3}}
\newcommand{\unitTime}{\color{c4}}
\newcommand{\perfectly}{\color{c5}}
\newcommand{\compounded}{\color{c6}}



\growth       The base for continuous growth
\plain        is
\\
\unitQuantity the unit quantity
\unitInterest earning unit interest
\unitTime     for unit time,
\\
\compounded   compounded
\perfectly    as fast as possible

Plain English

• What is e? A constant (2.718...) representing continuous unit growth: the unit quantity (1.0), continuously growing the unit rate (100%), for unit time (1 period).

• Why's e special? All circles are the unit circle, scaled up. All continuously growing systems are e^{rt}, scaled to some rate and time.

• When should I use e? Use e^{rt} for things that change constantly (radioactive decay, populations). For growth based on discrete intervals (interest payments, combinatorics), (1 + rate)^{time} is a better model.