Problem 88 - Elementary Algebra

Question

When the market opened on Monday morning, Garth bought some shares of a stock at \(\$ 13.25\) per share. The daily changes in the market for that stock for the week were \(0.75,-1.50,2.25,-0.25\), and \(-0.50\). What was the value of one share of that stock when the market closed on Friday afternoon?

Step-by-Step Solution

Answer

The stock's value per share on Friday was $14.00.

Step 1: Understand the Initial Price

The initial price per share when Garth bought the stock on Monday was \( \$13.25 \). This is the starting point for calculating how the price changes through the week as per the daily changes given.

Step 2: Apply Monday's Change

The first change is \( +0.75 \). Add this to the initial price:\[13.25 + 0.75 = 14.00.\]Thus, the price at the end of Monday is \( \$14.00 \).

Step 3: Apply Tuesday's Change

The change for Tuesday is \( -1.50 \). Subtract this from the Monday closing price:\[14.00 - 1.50 = 12.50.\]Therefore, the price at the end of Tuesday is \( \$12.50 \).

Step 4: Apply Wednesday's Change

On Wednesday, the change is \( +2.25 \). Add this to the Tuesday closing price:\[12.50 + 2.25 = 14.75.\]So the price at the end of Wednesday is \( \$14.75 \).

Step 5: Apply Thursday's Change

The change for Thursday is \( -0.25 \). Subtract this from the Wednesday closing price:\[14.75 - 0.25 = 14.50.\]Therefore, the price at the end of Thursday is \( \$14.50 \).

Step 6: Apply Friday's Change

The final change on Friday is \( -0.50 \). Subtract this from the Thursday closing price:\[14.50 - 0.50 = 14.00.\]Thus, the price at the end of Friday is \( \$14.00 \).

Key Concepts

Daily Price Changes

Understanding daily price changes in the stock market is crucial for tracking the value of investments over time. Every trading day, a stock can increase or decrease in value based on various factors like market demand, economic news, and investor sentiment.
In this problem, daily changes are given for a week:

• Monday: +0.75
• Tuesday: -1.50
• Wednesday: +2.25
• Thursday: -0.25
• Friday: -0.50

These changes are cumulative, meaning that each day's closing price becomes the following day's opening price. Such daily assessments help investors make timely and informed decisions about buying or selling stocks.

Initial Stock Price

The initial stock price is the first price at which a stock is bought or sold in a given context, and it serves as a baseline for any subsequent changes. In financial terms, this is often the price visible when the market opens.
In this exercise, Garth starts with an initial stock price of \(\$13.25\) per share on Monday morning. This is crucial because all the daily price movements will be determined relative to this initial value.
Starting with a known initial price enables investors to accurately track and calculate investment performance over time, providing a clear picture of gains or losses by the week's end.

Final Stock Price

Calculating the final stock price at the end of a given period involves sequentially applying all daily changes to the initial stock price. It's like peeling layers to see what lies at the core.
In this scenario, by the end of Friday, the cumulative effect of the week's price changes results in a final stock price of \(\$14.00\). This value indicates the stock's closing price after all price variations throughout the week are accounted for.
Tracking such final prices helps investors understand their financial position, decide on future actions, and compare past trends to make strategic decisions.

Arithmetic Operations

Arithmetic operations lie at the heart of this type of financial calculation, as each daily change is either added to or subtracted from the stock's current price.
For instance:

• The change on Monday is +0.75, which is added: \(13.25 + 0.75 = 14.00\).
• Tuesday's change of -1.50 requires subtraction: \(14.00 - 1.50 = 12.50\).
• The pattern continues with additions and subtractions for each day.

This method shows how simple arithmetic helps unravel the complex task of stock price calculation, allowing an investor to keep a constant check on how daily transactions influence the overall financial standing.