To determine the price of the stock after two years, we need to consider the initial price of the stock and the percentage appreciation in each of the two years.
1. Initial Price of the Stock:
The investor purchases shares at [tex]\( \$15 \)[/tex] per share.
2. First Year Appreciation:
The stock appreciates by 50% in the first year. To find the price at the end of the first year, we calculate:
[tex]\[
\text{Price after Year 1} = \text{Initial Price} \times (1 + \text{First Year Appreciation})
\][/tex]
[tex]\[
\text{Price after Year 1} = \$15 \times (1 + 0.50)
\][/tex]
[tex]\[
\text{Price after Year 1} = \$15 \times 1.50
\][/tex]
[tex]\[
\text{Price after Year 1} = \$22.50
\][/tex]
3. Second Year Appreciation:
The stock further appreciates by 10% in the second year. To find the price at the end of the second year, we calculate:
[tex]\[
\text{Price after Year 2} = \text{Price after Year 1} \times (1 + \text{Second Year Appreciation})
\][/tex]
[tex]\[
\text{Price after Year 2} = \$22.50 \times (1 + 0.10)
\][/tex]
[tex]\[
\text{Price after Year 2} = \$22.50 \times 1.10
\][/tex]
[tex]\[
\text{Price after Year 2} = \$24.75
\][/tex]
Therefore, the price of the stock after two years is [tex]\(\$24.75\)[/tex] per share.
The correct answer is:
[tex]\[ \boxed{\$24.75/share} \][/tex]
