Let's carefully analyze the given data and determine which person recovers their investment in a shorter amount of time.
### Step-by-Step Solution:
1. Calculate Foregone Earnings During College:
For each person, we compute the earnings they forsake by attending college. This is done by multiplying their salary prior to attending college by the number of years they spent in college.
Person A:
[tex]\[
\text{Forgone Earnings}_A = \$18{,}000 \times 3 = \$54{,}000
\][/tex]
Person B:
[tex]\[
\text{Forgone Earnings}_B = \$27{,}000 \times 4 = \$108{,}000
\][/tex]
2. Calculate Total Investment:
The total investment includes both the forgone earnings and the direct cost of college.
Person A:
[tex]\[
\text{Total Investment}_A = \text{Forgone Earnings}_A + \text{Cost of College}_A
= \$54{,}000 + \$45{,}000 = \$99{,}000
\][/tex]
Person B:
[tex]\[
\text{Total Investment}_B = \text{Forgone Earnings}_B + \text{Cost of College}_B
= \$108{,}000 + \$30{,}000 = \$138{,}000
\][/tex]
3. Calculate Time to Recover the Investment:
Divide the total investment by the salary upon graduation to determine how many years it will take for each person to recoup their investments.
Person A:
[tex]\[
\text{Time to Recover}_A = \frac{\text{Total Investment}_A}{\text{Salary Upon Graduation}_A} = \frac{\$99{,}000}{\$33{,}000} = 3 \text{ years}
\][/tex]
Person B:
[tex]\[
\text{Time to Recover}_B = \frac{\text{Total Investment}_B}{\text{Salary Upon Graduation}_B} = \frac{\$138{,}000}{\$37{,}000} \approx 3.73 \text{ years}
\][/tex]
4. Comparison:
Comparing the recovery times:
- Person A takes 3 years to recover their investment.
- Person B takes approximately 3.73 years to recover their investment.
Since Person A recovers their investment in a shorter amount of time compared to Person B, the true statement is:
a. Person A recovers their investment in a shorter amount of time.
