\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{jaydenroberts} \pdfinfo{ /Title (busn1009-quantitative-methods-cheat-sheet.pdf) /Creator (Cheatography) /Author (jaydenroberts) /Subject (BUSN1009 - Quantitative Methods 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}{B5B5B5} \definecolor{LightBackground}{HTML}{F5F5F5} \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{BUSN1009 - Quantitative Methods Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{jaydenroberts} via \textcolor{DarkBackground}{\uline{cheatography.com/19958/cs/2846/}}} \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}jaydenroberts \\ \uline{cheatography.com/jaydenroberts} \\ \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 9th May, 2016.\\ 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*}{3} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Tute 1}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{"If you get a positive value times a number, You need to shift the decimal to the right as many times as the number specified - If negative move it to the right. \newline % Row Count 4 (+ 4) Simple interest formula = S=FV=P(1 plus IK) \newline % Row Count 5 (+ 1) Compound interest formula = Sk = P (1 plus i)\textasciicircum{}k \newline % Row Count 6 (+ 1) Sn = P (1 plus I/T)\textasciicircum{}n \newline % Row Count 7 (+ 1) where I is interest \newline % Row Count 8 (+ 1) T is frequency of compounding per year \newline % Row Count 9 (+ 1) K is number of years \newline % Row Count 10 (+ 1) N is total number of periods - K {\emph{ T or T }} K \newline % Row Count 11 (+ 1) Depreciation Formula = Vo or P = Inital value, \newline % Row Count 12 (+ 1) Vk = P (1 - d)\textasciicircum{}k% Row Count 13 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Tute 4}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{1. Q = 24-3 p or p = 8 – Q/3 \newline % Row Count 1 (+ 1) 2. Q = 5p-8 or p = 1.6 + 0.2 Q \newline % Row Count 2 (+ 1) 3, either 24-3 p = 5 p-8 and p = 4 \newline % Row Count 3 (+ 1) or 8*Q/3 = 1.6 + 0.2 Q and Q = 12 \newline % Row Count 4 (+ 1) 4. TR = p ∙ Q = 8 Q – Q2/3 \newline % Row Count 5 (+ 1) MR = 8 – 2 Q/3 \newline % Row Count 6 (+ 1) 5. Max Π → MR = MC \newline % Row Count 7 (+ 1) 8 – 2Q/3 = Q/3 \newline % Row Count 8 (+ 1) Q = 8 \newline % Row Count 9 (+ 1) P = 8 – 8/3 = 5.33 \newline % Row Count 10 (+ 1) 6. Impose p≤ 3 – instead of equilibrium price p = 4 \newline % Row Count 12 (+ 2) Demand at p = 3 : QD = 24-3(3) = 15 \newline % Row Count 13 (+ 1) Supply at p = 3 : QS = 5(3) -8 = 7 \newline % Row Count 14 (+ 1) Excess demand = 15 – 7 = 8 \newline % Row Count 15 (+ 1) 7. AVC = 5 + 3 Q \newline % Row Count 16 (+ 1) TVC = (AVC) Q = 5 Q + 3 Q2 \newline % Row Count 17 (+ 1) 8. P = 18 – 3Q, MR = 18 – 6Q \newline % Row Count 18 (+ 1) 18 – 6Q = 12, Q = 1, p = 15% Row Count 19 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Tute 2}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{1. 5 years 1 + r = (FV/PV)1/5 \newline % Row Count 1 (+ 1) (i) r = 10.38\% \newline % Row Count 2 (+ 1) (ii) r = 10.47\% \newline % Row Count 3 (+ 1) (iii) r = 10.51\% \newline % Row Count 4 (+ 1) (iv) r = 10.52\% \newline % Row Count 5 (+ 1) (v) r = 10.52\% \newline % Row Count 6 (+ 1) 2. 1 + r = (1 + 0.06/12)8 ∙ (1 + 0.072/12)4 \newline % Row Count 7 (+ 1) 1 + r = (1.005)8 ∙ (1.006)4 \newline % Row Count 8 (+ 1) 1 + r = (1.0407) ∙ (1.0242) = 1.06591 \newline % Row Count 9 (+ 1) r = 6.59\% \newline % Row Count 10 (+ 1) For an initial outlay of \$1000 the net return is 1,000 (1.067) – 10 = 1,057. \newline % Row Count 12 (+ 2) Rate of return 5.7\% \newline % Row Count 13 (+ 1) For larger outlays, e.g. 10,000. 10,000 (1.067) – 10 = 10,660. \newline % Row Count 15 (+ 2) Rate of return 6.6\% \newline % Row Count 16 (+ 1) 3. 2500 = 97 (1 + r)40 Take logs of both sides. \newline % Row Count 17 (+ 1) Ln(2500/97) = 40Ln(1 + r) , or 3.249335 = 40Ln(1 + r), or Ln(1+ r) = 0.0812334 \newline % Row Count 19 (+ 2) Take the exponential of both sides: 1 + r = 1.084624 and r = 8.4624\% \newline % Row Count 21 (+ 2) 97 (1.0867)40 = 97 (27.822) = 2698.72 \newline % Row Count 22 (+ 1) Either (i)The rate of return is less than the bond rate or (ii) the \$97 would have grown to more than \$2,500 hence the purchase wasn't a good investment. \newline % Row Count 26 (+ 4) 4. (i) 10,000 \newline % Row Count 27 (+ 1) (ii) 10,000 (1.08)-2 = 10,000 (0.8573) = 8573.39 \newline % Row Count 28 (+ 1) (iii) 10,000 (1.08)-10 = 10,000 (0.4632) = 4631.93 \newline % Row Count 30 (+ 2) } \tn \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Tute 2 (cont)}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{5. (i) 1,050 (1.05)-1 = 1000 \newline % Row Count 1 (+ 1) (ii) 1,108 (1.05)-2 = 1004.99 (*) \newline % Row Count 2 (+ 1) (iii) 1,160 (1.05)-3 = 1002.05 \newline % Row Count 3 (+ 1) 6. PV = 10,000 (1.07)-2 + 5,000 (1.07)-3 + 15,000 (1.07)-5 \newline % Row Count 5 (+ 2) PV = 8,734.39 + 4,081.49 + 10,694.79 \newline % Row Count 6 (+ 1) PV = 23,510.67 \newline % Row Count 7 (+ 1) 7. 100,000 (1 + i )16 = 125,000 \newline % Row Count 8 (+ 1) 4 \newline % Row Count 9 (+ 1) (1 + i )16 = 1.25 → 1 + i = (1.25) 1/16 = 1.014044 \newline % Row Count 11 (+ 2) 4 4 \newline % Row Count 12 (+ 1) i = 0.0562 or 5.62\% \newline % Row Count 13 (+ 1) OR use logarithms \newline % Row Count 14 (+ 1) Ln{[}(1 + i/4)16{]} = Ln 1.25 and 16Ln( 1 + i/4) = 0.22314 \newline % Row Count 16 (+ 2) Ln( 1 + i/4) = 0.0139465 and 1 + i/4 = 1.014044. \newline % Row Count 18 (+ 2) 8. 15,000 (1 + 0.055)12 k = 30,000 \newline % Row Count 19 (+ 1) 12 \newline % Row Count 20 (+ 1) (1 + 0.055) 12 k = 2 \newline % Row Count 21 (+ 1) 12 \newline % Row Count 22 (+ 1) 12 k Ln (1 + 0.055) = Ln 2 \newline % Row Count 23 (+ 1) 12 \newline % Row Count 24 (+ 1) 12 k 0.0045728 = 0.69315 \newline % Row Count 25 (+ 1) k = 12.63 years. About 12 years and 7$\frac{1}{2}$ months.% Row Count 26 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Tute 3}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{1. Add up PV to get NPV \newline % Row Count 1 (+ 1) i = 6\% A B \newline % Row Count 2 (+ 1) -14,000 \newline % Row Count 3 (+ 1) 9.905.66 \newline % Row Count 4 (+ 1) 5,339.98 \newline % Row Count 5 (+ 1) 1,091.51 -15,000 \newline % Row Count 6 (+ 1) 943.40 \newline % Row Count 7 (+ 1) 5,161.98 \newline % Row Count 8 (+ 1) 11,754,67 \newline % Row Count 9 (+ 1) NVP (6\%): 2,337.14 2,860.05 (*) \newline % Row Count 10 (+ 1) i = 9\% A B \newline % Row Count 11 (+ 1) -14,000 \newline % Row Count 12 (+ 1) 9,633.03 \newline % Row Count 13 (+ 1) 5,050.08 \newline % Row Count 14 (+ 1) 1,003.84 -15,000 \newline % Row Count 15 (+ 1) 917.43 \newline % Row Count 16 (+ 1) 4,881.74 \newline % Row Count 17 (+ 1) 10,810.57 \newline % Row Count 18 (+ 1) NVP (9\%): 1,686.95 (*) 1,609.74 \newline % Row Count 19 (+ 1) 2. Find i such that NVP (i) = 0 \newline % Row Count 20 (+ 1) NVP (10\%) = -15,000 + 909.09 + 4,793.39 + 10,518.41 \newline % Row Count 22 (+ 2) NVP (10\%) = 1,220.89 \textgreater{} 0 \newline % Row Count 23 (+ 1) NVP (12\%) = -15,000 + 892.86 + 4,623.72 + 9,964.92 \newline % Row Count 25 (+ 2) NVP (12\%) = 481.51 \textgreater{} 0 \newline % Row Count 26 (+ 1) NVP (13\%) = -15,000 + 884.96 + 4,542.25 + 9,702.70 \newline % Row Count 28 (+ 2) NVP (13\%) = 129.91 \textgreater{} 0 \newline % Row Count 29 (+ 1) NVP (14\%) = -15,000 + 877.19 + 4,462.91 + 9,449.60 \newline % Row Count 31 (+ 2) } \tn \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Tute 3 (cont)}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{ NVP (14\%) = -210.29 \textless{} 0 \newline % Row Count 1 (+ 1) Say i is approximately i = 13.38\% \newline % Row Count 2 (+ 1) 3. PV = 150 {[}1 – (1 + 0.052 / 52)-156{]} \newline % Row Count 3 (+ 1) 0.052/52 \newline % Row Count 4 (+ 1) PV = 150 {[}1-0.8556{]} = 21,656.12 \newline % Row Count 5 (+ 1) 0.001 \newline % Row Count 6 (+ 1) 4. FV = 150 {[}(1.001)156 - 1{]} \newline % Row Count 7 (+ 1) 0.001 \newline % Row Count 8 (+ 1) FV = 150 {[}1.16873 - 1{]} = 25,310.26 \newline % Row Count 9 (+ 1) 0.001 \newline % Row Count 10 (+ 1) FV = PV (1.001)156 \newline % Row Count 11 (+ 1) 25,310.26 = 21,656.12 (1.16873) = 25,310.27 \newline % Row Count 12 (+ 1) Almost perfect match. \newline % Row Count 13 (+ 1) 5. (a) R = 120,000 (0.05/12) = 500 \newline % Row Count 14 (+ 1) {[}1 – (1 + 0.05)-120{]} {[}1 – 0.60716{]} \newline % Row Count 15 (+ 1) 12 \newline % Row Count 16 (+ 1) R = 1272.79 \newline % Row Count 17 (+ 1) (b) Outstanding Balance: B = 1272.79 {[}1 – (1 + 0.05) -96{]}/( 0.05/12) \newline % Row Count 19 (+ 2) 12 \newline % Row Count 20 (+ 1) B = 1272.79 {[}1-0.6709{]} = 100,536.97 \newline % Row Count 21 (+ 1) 0.05/12 \newline % Row Count 22 (+ 1) (c) New R = 100,536.97 (0.09/12) \newline % Row Count 23 (+ 1) {[}1 – (1 + 0.09) -96{]} \newline % Row Count 24 (+ 1) 12 \newline % Row Count 25 (+ 1) New R = 100,536.97 (0.0075) = 1472.89 \newline % Row Count 26 (+ 1) {[} 1 – 0.48806{]}% Row Count 27 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}