Question

Refer back to the ROI formula. Even if there were no parenthesis around the numerator (today's price - your price), explain why you would still carry out that subtraction first before the division and multiplication.

Answer 1

Subtraction is performed before division and multiplication in the ROI formula due to the precedence of the operations as determined by the BIDMAS or PEMDAS rules. Multiplication or Division and Addition or Subtraction have the same priority and are performed from left to right in an equation. This holds true in many areas, including financial mathematics calculations.

Step-by-step explanation:

The question refers to the arithmetic operation in the calculation of Return on Investment (ROI) and specifically to the priority of subtraction over division or multiplication, even without the presence of parentheses around the numerator. This is due to the order of operations in mathematics, often remembered with the acronym BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication and Division, Add and Subtract) - both grouped Division/Multiplication and Addition/Subtraction together, meaning they have the same priority level.

However, if multiplication or division and addition or subtraction exist together without brackets, then they are performed from left to right. So in the context of the ROI formula, regardless of parentheses, the subtraction will still be carried out first before any division or multiplication based on the order the operations appear in the formula: (Today's Price - Your Price) / Your Price.

This interpretation plays an important role in many fields, including financial mathematics where it's crucial for correct investments analysis, where a decimal point in a wrong place could mean significant changes in perceived profits or losses.

Learn more about Order of Operations

Answer 2

Question example:

Tori bought one share of Chipotle stock on Nov 1, 2016 for $396.33. Then, four years later, she sold it and the closing price for that day was $778.38.

a)How much money did she gain/lose with this stock?

b)What was Tori’s return on investment?

Answer and explanation:

The ROI(Return on investment) formula calculates the percentage return on the initial cost of investment.

To calculate return on investment, we must first calculate how much is gained or lost by subtracting price of investment when sold from price of investment when bought.

In the question above, the gain on the investment is gotten by subtracting closing price of Chipotle stock four years later $778.38 from price of Chipotle stock when it was bought on Nov 1, 2016 $396.33= $382.05

By getting our gain or loss on investment first, we are able to find the Return on investment(ROI) in percentage thus: $382.05/$396.33×100/1= 96.39%

We simply cannot divide first before subtraction because we need to get the gain or loss on investment and then express it as a percentage of the initial investment cost to get our ROI