Continuous Compounding in LaTeX (A = Pe^{rt})

Where it is used

Continuous compounding formula: principal P grows to Pe^{rt} after time t at continuously compounded rate r.

This is the limit of compound interest as compounding becomes infinitely frequent, since (1 + r/n)^{nt} \to e^{rt}. It is used throughout derivatives pricing, as in the discount factor e^{-rT} in the Black-Scholes formula. Brace the exponent, e^{rt}, so both letters are raised. Some styles set Euler's number upright, \mathrm{e}^{rt}, to distinguish it from a variable named e; either is accepted if consistent. For long exponents, \exp(rt) is easier to read than a tiny superscript, particularly with fractions in the exponent.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Continuous Compounding: $A = Pe^{rt}$

\[ A = Pe^{rt} \quad \Longrightarrow \quad P = A e^{-rt} \]
\end{document}

Related symbols

• Greater Than>
• Compound InterestA = P(1 + r/n)^{nt}
• Less Than<
• Present Value\frac{C}{(1+r)^t}
• Approximately Equal\approx
• Summation\sum_{t=1}^{n}

Frequently asked questions

How do I write Continuous Compounding in LaTeX?

Type A = Pe^{rt} in math mode, for example $A = Pe^{rt} \quad \Longrightarrow \quad P = A e^{-rt}$. It works in plain LaTeX without loading any package.

Which package do I need for A = Pe^{rt}?

None. A = Pe^{rt} is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use A = Pe^{rt} in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $A = Pe^{rt}$ in running text.