To determine which person recovers their investment in a shorter amount of time, we need to consider both the direct costs of college and the opportunity cost of lost wages while attending college. Here's a step-by-step breakdown:
1. Person A:
- Salary prior to college: \[tex]$18,000
- Years attending college: 3
- Total cost of college: \$[/tex]45,000
- Salary upon graduating: \[tex]$33,000
2. Person B:
- Salary prior to college: \$[/tex]27,000
- Years attending college: 4
- Total cost of college: \[tex]$30,000
- Salary upon graduating: \$[/tex]37,000
Next, let's calculate the total loss in salary for each person while they are in college.
Person A's loss of salary during college:
[tex]\[ \text{Loss Salary}_A = \text{Years Attending College}_A \times \text{Salary Prior}_A \][/tex]
[tex]\[ \text{Loss Salary}_A = 3 \times 18,000 \][/tex]
[tex]\[ \text{Loss Salary}_A = \$54,000 \][/tex]
Person B's loss of salary during college:
[tex]\[ \text{Loss Salary}_B = \text{Years Attending College}_B \times \text{Salary Prior}_B \][/tex]
[tex]\[ \text{Loss Salary}_B = 4 \times 27,000 \][/tex]
[tex]\[ \text{Loss Salary}_B = \$108,000 \][/tex]
Now, we sum the total cost of college and the loss of salary to find each person’s total investment.
Person A's total investment:
[tex]\[ \text{Total Investment}_A = \text{Loss Salary}_A + \text{Total Cost of College}_A \][/tex]
[tex]\[ \text{Total Investment}_A = 54,000 + 45,000 \][/tex]
[tex]\[ \text{Total Investment}_A = \$99,000 \][/tex]
Person B's total investment:
[tex]\[ \text{Total Investment}_B = \text{Loss Salary}_B + \text{Total Cost of College}_B \][/tex]
[tex]\[ \text{Total Investment}_B = 108,000 + 30,000 \][/tex]
[tex]\[ \text{Total Investment}_B = \$138,000 \][/tex]
To find out the time it takes for each person to recover their investment, we divide their total investment by their post-graduation salary.
Person A's recovery time:
[tex]\[ \text{Recovery Time}_A = \frac{\text{Total Investment}_A}{\text{Salary Upon Graduating}_A} \][/tex]
[tex]\[ \text{Recovery Time}_A = \frac{99,000}{33,000} \][/tex]
[tex]\[ \text{Recovery Time}_A = 3 \text{ years} \][/tex]
Person B's recovery time:
[tex]\[ \text{Recovery Time}_B = \frac{\text{Total Investment}_B}{\text{Salary Upon Graduating}_B} \][/tex]
[tex]\[ \text{Recovery Time}_B = \frac{138,000}{37,000} \][/tex]
[tex]\[ \text{Recovery Time}_B \approx 3.73 \text{ years} \][/tex]
Comparing the recovery times:
- Person A recovers their investment in approximately 3 years.
- Person B recovers their investment in approximately 3.73 years.
Therefore, the best answer is:
a. Person A recovers their investment in a shorter amount of time.
