Question

Caroline bought stock in a company two years ago that was worth xx dollars. During the first year that she owned the stock, it decreased by 21%. During the second year the value of the stock increased by 25%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

To find the value of the stock after the two years, we can start with the initial value of the stock, \( xx \).

1. **First Year:** The stock decreased by 21%. A decrease of 21% can be represented by multiplying the original value by \( 1 - 0.21 \) (which is \( 0.79 \)):
\[
\text{Value after year 1} = xx \times 0.79
\]

2. **Second Year:** The stock increased by 25% during the second year. An increase of 25% can be represented by multiplying the value at the end of the first year by \( 1 + 0.25 \) (which is \( 1.25 \)):
\[
\text{Value after year 2} = (xx \times 0.79) \times 1.25
\]

Now, we can simplify this expression:
\[
\text{Value after year 2} = xx \times 0.79 \times 1.25
\]

Calculating \( 0.79 \times 1.25 \):
\[
0.79 \times 1.25 = 0.9875
\]

So, the expression for the value of the stock after two years is:
\[
\text{Value after two years} = xx \times 0.9875
\]

Thus, the final expression in terms of \( xx \) is:
\[
0.9875xx
\]