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 23%. During the second year the value of the stock increased by 27%. 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 calculate the value at the end of each year based on the percentage increases.

1. After the first year: The stock increases by 23%. The value after the first year can be calculated as: \[ \text{Value after first year} = xx + (23% \text{ of } xx) = xx + 0.23xx = xx(1 + 0.23) = xx \times 1.23 \]

2. After the second year: The stock then increases by 27% based on the new value from the end of the first year. So, we calculate: \[ \text{Value after second year} = \text{Value after first year} + (27% \text{ of Value after first year}) \] \[ = (xx \times 1.23) + (0.27 \times (xx \times 1.23)) = xx \times 1.23 + 0.27xx \times 1.23 = xx \times 1.23(1 + 0.27) = xx \times 1.23 \times 1.27 \]

Now we calculate \(1.23 \times 1.27\): \[ 1.23 \times 1.27 = 1.5601 \]

Thus, the expression for the value of the stock after two years is: \[ \text{Value after two years} = xx \times 1.5601 \]

So, the final expression in terms of \(xx\) that represents the value of the stock after two years is: \[ \text{Value} = 1.5601xx \]