6.14.3: Formula Review
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
\(\begin{array}{l}p m t=\dfrac{P \times(r / 12) \times(1+r / 12)^{12 \times t}}{(1+r / 12)^{12 \times t}-1} \\ T=p m t \times 12 \times t \\ \mathrm{CoF}=T-P\end{array}\)