Math Problem Statement
Mary Reid invested $3,000 and borrowed $3,000 to purchase shares in JP Morgan Chase. At the time of her investment, Chase was selling for $140 a share.
If Mary paid a commission of $14, how many shares could she buy if she used only her own money and did not use margin?
Note: Round your answer to 1 decimal place.
If Mary paid a commission of $22, how many shares could she buy if she used her $3,000 and borrowed $3,000 on margin to buy Chase stock?
Note: Round your answer to 1 decimal place.
Assume Mary did use margin to buy her Chase stock. Also, assume she paid another $22 to sell her stock and sold the stock for $156 a share. How much profit did she make on her Chase stock investment?
Note: Round intermediate calculations to 1 decimal place. Round your final answer to 2 decimal places.
Solution
Part 1: Buying with only her own money (no margin)
Mary has $3,000 of her own money to invest, but she also needs to pay a commission of $14. Therefore, the total amount available to buy shares is:
The stock price is $140 per share, so the number of shares she can buy is:
Answer:
Mary could buy 21.3 shares if she used only her own money and did not use margin.
Part 2: Buying with $3,000 of her own money plus $3,000 on margin
Now, Mary has a total of $6,000 to invest ($3,000 of her own and $3,000 borrowed on margin). However, she must pay a $22 commission. Therefore, the total amount available to buy shares is:
At $140 per share, the number of shares she can buy is:
Answer:
Mary could buy 42.7 shares if she used her $3,000 and borrowed $3,000 on margin to buy Chase stock.
Part 3: Calculating profit if Mary sells at $156 per share
Mary purchased 42.7 shares and paid a total of $22 in commission to buy and another $22 in commission to sell. The selling price is $156 per share. First, let's calculate the revenue from selling the shares:
The total amount spent when buying the shares was:
The total commission paid is $22 when buying and $22 when selling, so:
Thus, the total profit is:
Final Answer:
Mary's total profit is $614.20.
Would you like more details or have any questions?
Here are 5 related questions:
- What are the risks associated with buying stocks on margin?
- How would the profit change if the stock price dropped to $130 instead of rising?
- How does paying commissions affect overall profitability in stock trading?
- How do margin requirements vary across different brokers?
- What is the formula for calculating percentage return on an investment?
Tip: Always consider both commissions and potential price fluctuations when making investments on margin.
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Math Problem Analysis
Mathematical Concepts
Arithmetic
Stock Market Investment
Profit Calculation
Formulas
Amount available = Total funds - Commission
Number of shares = Amount available / Stock price
Profit = Revenue from selling shares - Total cost - Commission fees
Theorems
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Suitable Grade Level
Grades 9-12
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