Question

Kevin bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it increased by 26%. During the second year the value of the stock decreased by 5%. 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 two years, we will calculate the changes in value step by step.

1. **After the first year:** The stock increases by 26%. The value at the end of the first year can be expressed as:
\[
\text{Value after first year} = xx + 0.26 \cdot xx = xx(1 + 0.26) = xx \cdot 1.26
\]

2. **After the second year:** The stock decreases by 5%. We need to apply this decrease to the value after the first year:
\[
\text{Value after second year} = \text{Value after first year} - 0.05 \cdot \text{Value after first year} = \text{Value after first year} (1 - 0.05)
\]
Substituting the value after the first year:
\[
\text{Value after second year} = (xx \cdot 1.26) \cdot (1 - 0.05) = (xx \cdot 1.26) \cdot 0.95
\]

3. **Combining the expressions:**
\[
\text{Value after two years} = xx \cdot 1.26 \cdot 0.95
\]

4. **Calculating the product:**
\[
1.26 \cdot 0.95 = 1.197
\]

So the final expression representing the value of the stock after two years is:
\[
\text{Value after two years} = xx \cdot 1.197
\]