Answer :
To determine the percentage increase required for Galen to get back to his initial investment of $12,000 after the stock price falls by 90%, we can follow these steps:
Initial Situation: Galen buys the stock for $12,000.
Loss Calculation: The stock price falls by 90% due to the negative news.
The amount lost can be calculated as:
[tex]\text{Amount Lost} = 0.90 \times 12,000 = 10,800[/tex]
Current Stock Value: With the loss calculated above, the current value of Galen's investment becomes:
[tex]\text{Current Value} = 12,000 - 10,800 = 1,200[/tex]
Required Increase Calculation: To find out how much the stock needs to increase to return to the original value of $12,000, we need to calculate the percentage increase based on the current value of $1,200:
The difference required to break even is:
[tex]\text{Difference Required} = 12,000 - 1,200 = 10,800[/tex]
The percentage increase required is then calculated as:
[tex]\text{Percentage Increase} = \left(\frac{10,800}{1,200}\right) \times 100\%[/tex]
Simplifying the fraction:
[tex]\text{Percentage Increase} = \left(9\right) \times 100\% = 900\%[/tex]
Therefore, the stock price must increase by 900% from its current value of $1,200 to return to the original investment value of $12,000.
