To determine how long it will take Brenda to recover her investment in obtaining a bachelor's degree, we need to compare the increase in her annual salary with the cost of getting the degree.
### Step-by-Step Solution:
1. Identify the median salaries:
- Median salary for associate's degree: \[tex]$38,000
- Median salary for bachelor's degree: \$[/tex]50,000
2. Calculate the difference between the salaries:
[tex]\[
\text{Difference in salaries} = \text{Median salary for bachelor's degree} - \text{Median salary for associate's degree}
\][/tex]
Plugging in the numbers:
[tex]\[
\text{Difference in salaries} = 50,000 - 38,000 = 12,000
\][/tex]
Brenda will earn \[tex]$12,000 more per year with a bachelor's degree compared to what she earns with an associate's degree.
3. Determine the cost of obtaining the bachelor's degree:
- Cost of bachelor's degree: \$[/tex]15,000
4. Calculate the time to recover the investment:
[tex]\[
\text{Recovery time} = \frac{\text{Cost of bachelor's degree}}{\text{Difference in salaries}}
\][/tex]
Using the values:
[tex]\[
\text{Recovery time} = \frac{15,000}{12,000} = 1.25 \text{ years}
\][/tex]
Therefore, it will take Brenda 1.25 years to recover her investment in obtaining a bachelor's degree.
