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 increased by 6%. During the second year the value of the stock decreased by 17%. 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 can break it down into two steps: the first year and the second year.

1. After the first year: The stock increases by 6%. If the original value is \(xx\), the value of the stock after the first year can be calculated as:

   \[ \text{Value after Year 1} = xx + 0.06 \cdot xx = xx(1 + 0.06) = xx(1.06) \]

2. After the second year: The stock value decreases by 17%. We take the value after the first year and decrease it by 17%. The value after the second year can be calculated as:

   \[ \text{Value after Year 2} = \text{Value after Year 1} - 0.17 \cdot \text{Value after Year 1} \]

   This can be expressed as:

   \[ \text{Value after Year 2} = \text{Value after Year 1} (1 - 0.17) = \text{Value after Year 1} \cdot 0.83 \]

   Substituting the value after the first year:

   \[ \text{Value after Year 2} = xx(1.06) \cdot 0.83 \]

Now we can combine these calculations:

\[ \text{Value after Year 2} = xx \cdot 1.06 \cdot 0.83 \]

Calculating \(1.06 \times 0.83\):

\[ 1.06 \times 0.83 = 0.878 \]

Thus, the expression that represents the value of the stock after two years is:

\[ \text{Value after two years} = xx \cdot 0.878 \]

So, the final expression is:

\[ \text{Value after two years} = 0.878xx \]