Question

Sadie 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 22%. During the second year the value of the stock increased 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 calculate the value of the stock after two years, we can apply the percentage increases step by step.

1. **First Year Increase**: The stock increases by 22%. Hence, the value at the end of the first year can be represented as:
\[
\text{Value after Year 1} = xx + (0.22 \times xx) = xx \times (1 + 0.22) = xx \times 1.22
\]

2. **Second Year Increase**: In the second year, the value of the stock increases by 5% from its end of year 1 value. Therefore, the value at the end of the second year can be expressed as:
\[
\text{Value after Year 2} = \text{Value after Year 1} + (0.05 \times \text{Value after Year 1}) = (xx \times 1.22) + (0.05 \times (xx \times 1.22))
\]
This can be further simplified:
\[
\text{Value after Year 2} = xx \times 1.22 \times (1 + 0.05) = xx \times 1.22 \times 1.05
\]

Putting it all together, the final expression for the value of the stock after two years is:
\[
\text{Value after 2 Years} = xx \times 1.22 \times 1.05
\]

Calculating \( 1.22 \times 1.05 \):
\[
1.22 \times 1.05 = 1.281
\]

Thus, the expression simplifies to:
\[
\text{Value after 2 Years} = xx \times 1.281
\]

This is the expression in terms of \( xx \) that represents the value of the stock after two years have passed.