Present Value in LaTeX (\frac{C}{(1+r)^t})

Where it is used

Present value of a single cash flow C received at time t, discounted at rate r per period.

Discounting divides a future amount by the growth factor (1+r)^t, so 1,000 received in 3 years at 5% is worth about 863.84 today. Summing this term over periods gives NPV and bond prices. In display math \frac draws a full-size fraction; in inline text it shrinks, so \tfrac or a slash form C/(1+r)^t may read better. If the denominator becomes complex, for example with a varying rate (1 + r_t), use \prod or keep the exponent in braces: ^{t} matters when t is more than one character, like ^{t-1}.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Present Value: $\frac{C}{(1+r)^t}$

\[ PV = \frac{C}{(1+r)^t} = \frac{1000}{(1.05)^3} \approx 863.84 \]
\end{document}

Related symbols

• Compound InterestA = P(1 + r/n)^{nt}
• Summation\sum_{t=1}^{n}
• Continuous CompoundingA = Pe^{rt}
• ROI\text{ROI}
• Greater Than>
• IRR\text{IRR}

Frequently asked questions

How do I write Present Value in LaTeX?

Type \frac{C}{(1+r)^t} in math mode, for example $PV = \frac{C}{(1+r)^t} = \frac{1000}{(1.05)^3} \approx 863.84$. It works in plain LaTeX without loading any package.

Which package do I need for \frac{C}{(1+r)^t}?

None. \frac{C}{(1+r)^t} is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \frac{C}{(1+r)^t} in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\frac{C}{(1+r)^t}$ in running text.