To determine the profit Caroline would make if she sold all her shares, we need to carefully go through the cost price, selling price, and calculate the difference between these two values. Here is the step-by-step breakdown:
1. Determine the initial price per share:
Caroline bought each share at [tex]\( \frac{101}{2} \)[/tex] dollars.
[tex]\[
\text{Initial price per share} = 50.5 \text{ dollars}
\][/tex]
2. Calculate the total cost price of the shares:
Caroline bought 20 shares. So, the total cost price is:
[tex]\[
\text{Cost Price} = 20 \times 50.5 = 1010.0 \text{ dollars}
\][/tex]
3. Determine the value of each share after 10 months:
After 10 months, the value of each share is [tex]\( 11^{\frac{1}{4}} \)[/tex].
[tex]\[
\text{Final price per share} = 1.8211602868378718 \text{ dollars}
\][/tex]
4. Calculate the total selling price of the shares:
If Caroline sells all 20 shares at the new price per share:
[tex]\[
\text{Selling Price} = 20 \times 1.8211602868378718 = 36.42320573675744 \text{ dollars}
\][/tex]
5. Determine the profit or loss:
Profit is calculated as:
[tex]\[
\text{Profit} = \text{Selling Price} - \text{Cost Price}
\][/tex]
[tex]\[
\text{Profit} = 36.42320573675744 - 1010.0 = -973.5767942632426 \text{ dollars}
\][/tex]
As we can see, Caroline would actually incur a loss rather than a profit. Thus, none of the options A, B, C, D correspond to the correct financial result (which is a loss of approximately -\$973.58). Therefore, this question may contain a set of options that do not include the correct answer.
