Let's work through Aaron's situation step-by-step to determine how long it will take him to recover the investment he makes in obtaining an associate's degree.
### Step 1: Understand the Given Data
1. Current Salary (High School Graduate):
- Median salary for a high school graduate: [tex]$30,000 per year
2. Future Salary (Associate's Degree):
- Median salary for someone with an associate's degree: $[/tex]40,000 per year
3. Cost of College:
- Total cost to complete an associate's degree: [tex]$30,000
### Step 2: Calculate the Additional Earnings
The additional earnings Aaron would obtain by having an associate’s degree are:
\[
\text{Additional Earnings Per Year} = \text{Median Salary (Associate's Degree)} - \text{Median Salary (High School Graduate)}
\]
Substituting the values:
\[
\text{Additional Earnings Per Year} = \$[/tex]40,000 - \[tex]$30,000 = \$[/tex]10,000
\]
### Step 3: Calculate the Time to Recover the Investment
Next, we need to determine how many years it will take Aaron to recover the [tex]$30,000 he invested in his education. This can be done using the formula:
\[
\text{Years to Recover Investment} = \frac{\text{Total College Cost}}{\text{Additional Earnings Per Year}}
\]
Substituting the values:
\[
\text{Years to Recover Investment} = \frac{\$[/tex]30,000}{\$10,000} = 3 \text{ years}
\]
### Conclusion
Therefore, if Aaron decides to go to college and completes his associate's degree in 2 years, it will take him approximately 3 years to recover his college investment from the additional earnings he will make due to his higher salary after obtaining the degree.
