Mathematical Concept Guide

MATHEMATICAL CONCEPT GUIDE The following guide, if needed, serves as a refresher of some of the arithmetic and basic algebra necessary to solve some of the financial calculations required throughout this course. •

Rule for Order of Operations 1. 2. 3. 4. 5. 6.

Parentheses (perform work inside parentheses first) Exponents (simplify (simplif y exponents) Multiplication Multiplic ation (left to right) Division (left to right) Addition (left to right) Subtraction (left to right) 3 + 4 x (1 + 0.05) 2 = 3 + 4 x (1.05 ( 1.05))2 = 3 + 4 x 1.1025 = 3 + 4.41 = 7.41

Some students may recall memorising the order of operations as “ PEMDAS.” PEMDAS.” •

Exponents Exponents are used to help condense the steps involved in multiplication, which is especially helpful when compounding. For example, when multiplying 1.05 times itself 5 times, we could perform the following calculation: 1.05 x 1.05 x 1.05 x 1.05 x 1.05 = 1.28 (rounded) We could also simplify the problem by writing (1.05)5 to get the same answer. Also, in Excel you can enter this into any cell as follows: =1.05^5

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Percentages Percentages in decimal form appear differently than when written with a percent sign. For example, 5% is written as 0.05 in decimal form. However, please note that the percent sign is not included when the percentage appears in decimal form. Including the percent sign would make 0.05% really equate to 0.0005 and can lead to errors in calculations. Also, please note that for all financial calculations, you must have at least 4 decimal places to eliminate rounding errors.

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Basic Statistic Definitions Mean—The sum of a set of values divided by the number of values Median—The middle value of a set of values arranged in order of magnitude Mode—The value that occurs most frequently Delta ( ∆)—Denotes change (% of  ∆ in Demand / % of  ∆ in Price to calculate Price elasticity of Demand)

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Graphing Graphs are often used to better demonstrate measurements and relationships. A variety of graphs may be used, and each serves a different function: Cartesian Coordinate System—Uses the horizontal axis ( x ) and vertical axis ( y ) to plot points on a two-dimensional graph. In the example below, the point at which the axes intersect is zero (0) and the positive and negative areas of each quadrant are identified. y  x  = – y  = +

x  = + y  = +

x  x  = – y  = –

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x  = + y  = –

Relationships Direct Relationship: y  = kx , where k is a constant. If x increases, then y increases. If x  decreases, then y decreases as well. In economics, the law of supply represents a direct relationship—as price increases, the quantity supplied increases. An example of a Supply Curve is shown in red in the form of a positively sloped line. Price

Quantity Indirect or Inverse Relationship: y  = k /x , where k is a constant. If x increases, then y  decreases. If x decreases, then y increases. In economics, the law of demand represents an indirect relationship—as price increases, the quantity demanded decreases. An example of a Demand Curve is shown in red in a negatively sloped line. Price

Quantity