Sure, let's break down the problem step-by-step to determine how long it will take Aaron to recover his investment by obtaining an associate's degree.
1. First, we need to know the median annual salary for a high school graduate. According to the given data, the median annual salary for high school graduates in 1997 is \[tex]$30,400.
2. Next, we need the median annual salary for someone with an associate's degree. This is given as \$[/tex]37,400.
3. Calculate the additional annual income Aaron would earn with an associate's degree:
[tex]\[
\text{Additional Annual Income} = \text{Salary with Associate's Degree} - \text{Salary with High School Degree}
\][/tex]
[tex]\[
\text{Additional Annual Income} = 37,400 - 30,400 = \$7,000
\][/tex]
4. Aaron's total college costs amount to \[tex]$30,000.
5. To determine how long it will take Aaron to recover his investment, we divide the total college costs by the additional annual income:
\[
\text{Time to Recover Investment} = \frac{\text{Total College Costs}}{\text{Additional Annual Income}}
\]
\[
\text{Time to Recover Investment} = \frac{30,000}{7,000} \approx 4.285714285714286 \text{ years}
\]
To summarize, Aaron will take approximately \(4.29\) years to recover the \$[/tex]30,000 investment he made for his associate's degree based on the increase in his median annual salary.
