7.S: Summary
- Page ID
- 22107
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Key Concepts Summary
7.1: Sales Taxes (Everybody Wants a Piece of My Pie)
- The three sales taxes, current rates, and how to calculate prices including taxes
- How businesses complete GST/HST remittances
7.2: Property Taxes (I Owe, I Owe)
- How municipalities levy mill rates and tax rates against real estate owners
7.3: Exchange Rates and Currency Exchange (It Is a Global World)
- Converting currencies through exchange rates
- The rise and decline of exchange rates: currency appreciation and depreciation
7.4: Invoicing: Terms of Payment and Cash Discounts (Make Sure You Bill Them)
- How invoicing works: understanding invoice terms and invoice dating
- The calculations involved when a full payment amount is made
- The calculations involved when a partial payment amount is made
- The calculations involved when a late payment amount is made
The Language of Business Mathematics
- assessed value
-
The portion of the market value of a property that is subject to municipal taxes.
- buy rate
-
The rate at which a foreign currency is bought; it will always be lower than the mid-rate in terms of money per unit of foreign currency.
- cash discount
-
A percentage of the balance owing on an invoice that can be deducted for payment received either in full or in part during the discount period.
- credit period
-
The number of interest-free days from the date of commencement before full payment of the invoice is required.
- currency appreciation
-
When one currency strengthens relative to another currency, resulting in an ability to purchase more of that other currency than it could previously.
- currency depreciation
-
When one currency weakens relative to another currency, resulting in an ability to purchase less of that other currency than it could previously.
- date of commencement
-
The first day from which the invoice terms extend forward in time and from which all due dates are established.
- discount period
-
The number of days from the date of commencement for which a cash discount is offered.
- end-of-month invoice dating
-
A term of payment where the date of commencement is the last day of the same month as indicated by the invoice date.
- exchange rate
-
The number of units of a foreign currency that are bought with one unit of the domestic currency, or vice versa.
- GST
-
The goods and services tax is a Canadian federal sales tax on most products purchased by businesses and consumers alike.
- HST
-
The harmonized sales tax is a tax that combines the GST and PST into a single tax.
- market value
-
A snapshot of the estimated selling price of a property at some specified point in time.
- mid-rate
-
An exchange rate that does not involve or provide for any charges for currency conversion.
- mill rate
-
A tax per $1,000 of assessed value to determine property taxes.
- ordinary invoice dating
-
A term of payment where the date of commencement is the same date as the invoice date.
- property taxes
-
Annual taxes paid by the owners of real estate to local levying authorities to pay for services such as roads, water, sewers, public schools, policing, fire departments, and other community services.
- PST
-
The provincial sales tax is a consumer sales tax administered by Canadian provinces and territories.
- receipt-of-goods invoice dating
-
A term of payment where the date of commencement is the day on which the customer physically receives the goods.
- sales tax
-
A percent fee levied by a government on the supply of products.
- sell rate
-
The rate at which a foreign currency is sold. It is always higher than the mid-rate in terms of money per unit of foreign currency.
- tax policy
-
A municipality-based percentage of the market value of a property that is used to convert the market value into an assessed value.
- tax rate
-
A tax per $100 of assessed value to determine property taxes.
- tax remittance
-
The fulfillment of a tax obligation.
The Formulas You Need to Know
Symbols Used
\(AV\) = assessed value of a property
Current Currency = currency you are converting from
Desired Currency = currency you are converting to
Exchange Rate = per-unit conversion rate for current currency
Property Tax = property tax amount
\(PTR\)= property tax rate, usually set on a per $100 (tax rate) or per $1,000 (mill rate) basis
Rate = sales tax
Remit = tax remittance
\(S\) = selling price
\(S_{tax}\) = selling price including taxes
Tax Collected = total tax collected through sales
Tax Paid = total tax paid through purchases
Formulas Introduced
Formula 7.1 Selling Price Including Tax: \(S_{tax}=S+(S \times \text { Rate })\)
Formula 7.2 GST/HST Remittance: \(\text{Remit }=\text{ Tax Collected }-\text{ Tax Paid}\)
Formula 7.3 Property Taxes: \(\text { Property Tax }=\Sigma(AV \times PTR)\)
Formula 7.4 Currency Exchange: \(\text{Desired Currency }=\text{ Exchange Rate } \times \text{ Current Currency}\)
Technology
Calculator
The Percent Change function is used in this chapter. See the end of Chapter 3 for a full discussion on this calculator function.