Let's solve the problem step-by-step.
1. Opportunity Cost Calculation:
- Person A:
- Salary prior to school: $18,000
- Years attending college: 3
- Opportunity cost = Salary prior to school Years attending college
- \( \text{Opportunity cost for Person A} = 18,000 \times 3 = 54,000 \)
- Person B:
- Salary prior to school: $27,000
- Years attending college: 4
- Opportunity cost = Salary prior to school Years attending college
- \( \text{Opportunity cost for Person B} = 27,000 \times 4 = 108,000 \)
2. Total Investment Calculation:
- Person A:
- Opportunity cost: $54,000
- Total cost of college: $45,000
- Total investment = Opportunity cost + Total cost of college
- \( \text{Total investment for Person A} = 54,000 + 45,000 = 99,000 \)
- Person B:
- Opportunity cost: $108,000
- Total cost of college: $30,000
- Total investment = Opportunity cost + Total cost of college
- \( \text{Total investment for Person B} = 108,000 + 30,000 = 138,000 \)
3. Time to Recover the Investment Calculation:
- Person A:
- Total investment: $99,000
- Salary upon graduating: $33,000
- Salary prior to school: $18,000
- Increment in salary: [tex]$33,000 - $[/tex]18,000 = $15,000
- Time to recover investment = Total investment / Increment in salary
- \( \text{Time to recover for Person A} = \frac{99,000}{15,000} = 6.6 \) years
- Person B:
- Total investment: $138,000
- Salary upon graduating: $37,000
- Salary prior to school: $27,000
- Increment in salary: [tex]$37,000 - $[/tex]27,000 = $10,000
- Time to recover investment = Total investment / Increment in salary
- \( \text{Time to recover for Person B} = \frac{138,000}{10,000} = 13.8 \) years
Based on the calculations above:
- Person A recovers their investment in 6.6 years.
- Person B recovers their investment in 13.8 years.
Therefore, the true statement is:
a. Person A recovers their investment in a shorter amount of time.
