To determine which person recovers their investment in a shorter amount of time, we need to calculate the following for both individuals:
1. Opportunity cost (lost salary while attending college).
2. Total cost of college (sum of opportunity cost and direct cost of college).
3. Time taken to recover the investment (total cost divided by the increase in salary after graduation).
Let's break it down step-by-step for both Person A and Person B.
### For Person A:
1. Salary prior to college: [tex]$18,000 per year
2. Years attending college: 3 years
3. Total cost of college: $[/tex]45,000
4. Salary upon graduating: [tex]$33,000 per year
#### Calculations:
- Opportunity cost (lost salary during college):
\[
18,000 \, \text{dollars/year} \times 3 \, \text{years} = 54,000 \, \text{dollars}
\]
- Total cost of college:
\[
54,000 \, \text{dollars (opportunity cost)} + 45,000 \, \text{dollars (cost of college)} = 99,000 \, \text{dollars}
\]
- Increase in salary upon graduating:
\[
33,000 \, \text{dollars} - 18,000 \, \text{dollars} = 15,000 \, \text{dollars/year}
\]
- Time to recover the investment:
\[
\frac{99,000 \, \text{dollars}}{15,000 \, \text{dollars/year}} = 6.6 \, \text{years}
\]
### For Person B:
1. Salary prior to college: $[/tex]27,000 per year
2. Years attending college: 4 years
3. Total cost of college: [tex]$30,000
4. Salary upon graduating: $[/tex]37,000 per year
#### Calculations:
- Opportunity cost (lost salary during college):
[tex]\[
27,000 \, \text{dollars/year} \times 4 \, \text{years} = 108,000 \, \text{dollars}
\][/tex]
- Total cost of college:
[tex]\[
108,000 \, \text{dollars (opportunity cost)} + 30,000 \, \text{dollars (cost of college)} = 138,000 \, \text{dollars}
\][/tex]
- Increase in salary upon graduating:
[tex]\[
37,000 \, \text{dollars} - 27,000 \, \text{dollars} = 10,000 \, \text{dollars/year}
\][/tex]
- Time to recover the investment:
[tex]\[
\frac{138,000 \, \text{dollars}}{10,000 \, \text{dollars/year}} = 13.8 \, \text{years}
\][/tex]
By comparing both calculated recovery times:
- Person A: 6.6 years
- Person B: 13.8 years
### Conclusion:
Person A recovers their investment in a shorter amount of time. Therefore, the correct option is:
a. Person A recovers their investment in a shorter amount of time.
