\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{MJ McGiver}
\pdfinfo{
  /Title (115-114-finance-fundamentals.pdf)
  /Creator (Cheatography)
  /Author (MJ McGiver)
  /Subject (115.114 Finance Fundamentals Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{679996}
\definecolor{LightBackground}{HTML}{F5F8F8}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{115.114 Finance Fundamentals Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{MJ McGiver} via \textcolor{DarkBackground}{\uline{cheatography.com/213568/cs/46481/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}MJ McGiver \\
  \uline{cheatography.com/mj-mcgiver} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 28th May, 2025.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{2.96 cm} x{5.04 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Chpt4. TVM-Single Payments}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Time Value of money}} & {\emph{Individuals prefer to receive a dollar today to receiving that same dollar promised in a year's time.}} \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{8.4cm}}{} \tn 
% Row Count 5 (+ 0)
% Row 2
\SetRowColor{LightBackground}
{\bf{Interest}} & {\emph{The cost of funds to a borrower or part of the return for a lender or investor}} \tn 
% Row Count 9 (+ 4)
% Row 3
\SetRowColor{white}
{\bf{Mortgage}} & {\emph{recover money by selling property}} \tn 
% Row Count 11 (+ 2)
% Row 4
\SetRowColor{LightBackground}
{\bf{Term Loan}} & {\emph{bank loan with maturity\textasciicircum{}due date\textasciicircum{}}} \tn 
% Row Count 13 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.56 cm} x{5.44 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{4.1 Simple Interest \& Future Value}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Future Value}} & {\emph{amount received later}}; cash value of investment at future date: `FV=P(1+rn)` \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Simple Interest}} & {\emph{Interest calculated on the original amount}}: `I=(P)(r)(n)` \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
{\bf{Money Markets}} & {\emph{short-term debt markets}}: companies can borrow/ invest in the short-term. \tn 
% Row Count 9 (+ 3)
% Row 3
\SetRowColor{white}
{\bf{Formula}} & `FV = P(1 + rn)` \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.4 cm} x{5.6 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{4.2 Simple Interest \& Present Value}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Present Value}} & {\emph{amount today}}: needed cash today, to yield a particular value at future. \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Discounts}} & {\emph{to find the present value of future amount}}: inverse for compounding interest. \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
{\bf{Formula}} & `PV = FV/(1+rn)` \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{Working out/ Calculating how much the money we expect to receive in the future is worth today.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.96 cm} x{5.04 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{4.3 Compound Interest \& FV}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Compounded Interest}} & {\emph{Interest is stacking}}: It is then added to the principal \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Compounding}} & {\emph{Process of finding future amounts where interest is paid on interest already earned.}} \tn 
% Row Count 7 (+ 4)
% Row 2
\SetRowColor{LightBackground}
{\bf{Opportunity Cost}} & {\emph{best market yield achieve through alternative course of action}}: Market Yield is often benchmarked for opportunity costs \tn 
% Row Count 12 (+ 5)
% Row 3
\SetRowColor{white}
{\bf{Formula}} & `FV = PV(1+r)\textasciicircum{}n\textasciicircum{}` \tn 
% Row Count 13 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{Working out/ calculating future value through interest for each period (plus any interest), then added to the principal.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.16 cm} x{5.84 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{4.4 PV of a single payment}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Discounting}} & {\emph{The process of finding current amounts by the process of present value.}} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Formula}} & `PV = FV / (1+r)\textasciicircum{}n\textasciicircum{}` \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Formula2}} & `PV = FV x (1+r)\textasciicircum{}-n\textasciicircum{}` \tn 
% Row Count 7 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.72 cm} x{5.28 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{4.5 Compounding frequency}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Coupon}} & {\emph{Interest paid, based on a percentage of a bond's face value.}} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Zero- coupon Bond}} & {\emph{single-payment}}: no interest payment during its lifetime since interest is included with the repayment of principal at maturity. \tn 
% Row Count 8 (+ 5)
% Row 2
\SetRowColor{LightBackground}
{\bf{Maturity}} & {\emph{Deadline}}:The date when security will be payed. \tn 
% Row Count 10 (+ 2)
% Row 3
\SetRowColor{white}
{\bf{Formula}} & `FV = PV x (1 + r/m)\textasciicircum{}m x n\textasciicircum{}` \tn 
% Row Count 12 (+ 2)
% Row 4
\SetRowColor{LightBackground}
{\bf{Formula2}} & `PV = FV / (1 + r/m)\textasciicircum{}m x n\textasciicircum{}` \tn 
% Row Count 14 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{When compounding period per year is increased by {\emph{semi-annually, quarterly, monthly or daily.}} \newline  \newline PV formula can be used to calculate the current value of a zero-coupon bond.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.48 cm} x{5.52 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{4.6 Continuous compounding/ discounting}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Formula}} & `FV = PV (PV x e\textasciicircum{}r x n\textasciicircum{})` \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
{\bf{or}} & `FV = PVe\textasciicircum{}rn\textasciicircum{}` \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{When compounding frequency is increased to a very large number of (infinity). \newline  \newline Where e is constant, e = 2.718}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{4.7 Nominal \& Effective Interest Rates}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Nominal Rate}} & {\emph{contractual rate, ignores compounding. includes inflation}}: quoted rate \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
{\bf{Effective Rate}} & {\emph{actual rate, accounts compounding. includes adjustments}}: adjustments to nominal rate for the frequency of compounding. \tn 
% Row Count 10 (+ 6)
% Row 2
\SetRowColor{LightBackground}
{\bf{Annual Percentage Rate (APR)}} & {\emph{contractual rate, ignores compounding. when short-term rates are annualized }} \tn 
% Row Count 14 (+ 4)
% Row 3
\SetRowColor{white}
{\bf{Rate of Return}} & {\emph{rate of profit/ loss from investment}} \tn 
% Row Count 16 (+ 2)
% Row 4
\SetRowColor{LightBackground}
{\bf{Formula}} & `r\textasciitilde{}e\textasciitilde{} = (1 + r/m)\textasciicircum{}m\textasciicircum{} - 1` \tn 
% Row Count 18 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.64 cm} x{5.36 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{4.8 Unknown Interest Rate}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Formula}} & `r = (FV/PV)\textasciicircum{}1/n\textasciicircum{} - 1` \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{FV and PV is given, but find interest rate.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}