6.14.3: Formula Review
- Page ID
- 129589
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Formula Review
6.1 Understanding Percent
part \(=\) percent \(x\) total
6.2 Discounts, Markups, and Sales Tax
discount \(=\) percent discount \(\times\) original price
sale price \(=\) original price - discount
sale price \(=\) original price - percent discount \(\times\) original price \(=\) original price \(\times(1-\) percent discount \()\)
markup \(=\) percent markup \(\times\) cost
retail price \(=\) cost + markup
retail price \(=\) cost + percent markup \(\times\) cost \(=\) cost \(\times(1+\) percent markup \()\)
sales tax \(=\) purchase price \(\times\) tax rate
Total price \(=\) purchase price + purchase price \(\times\) tax rate \(=\) purchase price \(\times(1+\) tax rate \()\)
6.3 Simple Interest
\(\begin{array}{l}I=P \times r \times t \\ T=P+I \\ T=P+P \times r \times t \\ I=P \times \dfrac{r}{365} \times t \\ F V=P+I=P+P \times r \times t \\ A=P \times \dfrac{r \times(1+r)^t}{(1+r)^t-1} \\ P V=\dfrac{F V}{(1+r t)}\end{array}\)
6.4 Compound Interest
\(\begin{array}{l}A=P\left(1+\dfrac{r}{n}\right)^{n t} \\ P V=\dfrac{A}{\left(1+\dfrac{r}{n}\right)^{n \times t}} \\ Y=\left(1+\dfrac{r}{n}\right)^n-1\end{array}\)
6.6 Methods of Savings
\(\begin{array}{l}A=P\left(1+\dfrac{r}{n}\right)^{n t} \\ \mathrm{ROI}=\dfrac{F V-P}{P} \\ F V=p m t \times \dfrac{(1+r / n)^{n \times t}-1}{r / n} \\ p m t=\dfrac{F V \times(r / n)}{(1+r / n)^{n \times t}-1}\end{array}\)
6.7 Investments
\(\begin{array}{l}\text { annual return }=\left(\dfrac{F V}{P}\right)^{\left(\dfrac{1}{t}\right)}-1 \\ \mathrm{P} / \mathrm{E}=\dfrac{\text { Share Price }}{\text { Dividend }} \\ \mathrm{Yld} \%=\dfrac{\text { Annual Dividend }}{\text { Share Price }} \times 100 \%\end{array}\)
6.8 The Basics of Loans
\(\begin{array}{l}I=P \times \dfrac{r}{n} \\ p m t=\dfrac{P \times(r / n) \times(1+r / n)^{n \times t}}{(1+r / n)^{n \times t}-1}\end{array}\)
6.9 Understanding Student Loans
funding gap = total cost - all aid
\(\begin{array}{l}A=P\left(1+\frac{r}{n}\right)^{n t} \\ p m t=\frac{P \times(r / n) \times(1+r / n)^{n \times t}}{(1+r / n)^{n \times t}-1}\end{array}\)
discretionary income \(=\) gross income \(-1.5 \times\) poverty guideline
6.10 Credit Cards
\(I=\dfrac{\mathrm{ADB} \times r \times d}{365}\)
6.11 Buying or Leasing a Car
\(\begin{array}{l}p m t=\dfrac{P \times(r / n) \times(1+r / n)^{n \times t}}{(1+r / n)^{n \times t}-1} \\ \mathrm{MD}=\dfrac{P-R}{n} \\ \mathrm{APR}=2400 \times \mathrm{MF} \\ \mathrm{MF}=\mathrm{APR} / 2,400 \\ P M T=\dfrac{(P-R)}{n}+(P+R) \times \mathrm{MF}\end{array}\)
6.12 Renting and Home Ownership
\(\begin{array}{l}p m t=\dfrac{P \times(r / 12) \times(1+r / 12)^{12 \times t}}{(1+r / 12)^{12 \times t}-1} \\ T=p m t \times 12 \times t \\ \mathrm{CoF}=T-P\end{array}\)