To determine who recovers their investment in education in a shorter amount of time, we need to analyze the data given:
1. Person A:
- Salary prior to school: \[tex]$18,000
- Years attending college: 3 years
- Total cost of college: \$[/tex]45,000
- Salary upon graduating: \[tex]$33,000
2. Person B:
- Salary prior to school: \$[/tex]27,000
- Years attending college: 4 years
- Total cost of college: \[tex]$30,000
- Salary upon graduating: \$[/tex]37,000
To solve this, let's go through the calculations step-by-step:
### 1. Determining Lost Salary During College
This is the salary they would have earned if they hadn't attended college, over the years they were attending college.
- Person A:
[tex]\[ \text{Lost salary} = 18,000 \, \text{USD/year} \times 3 \, \text{years} = 54,000 \, \text{USD} \][/tex]
- Person B:
[tex]\[ \text{Lost salary} = 27,000 \, \text{USD/year} \times 4 \, \text{years} = 108,000 \, \text{USD} \][/tex]
### 2. Determining the Total Investment in Education
This includes both the lost salary and the cost of college.
- Person A:
[tex]\[ \text{Total investment} = \text{Lost salary} + \text{Cost of college} = 54,000 \, \text{USD} + 45,000 \, \text{USD} = 99,000 \, \text{USD} \][/tex]
- Person B:
[tex]\[ \text{Total investment} = \text{Lost salary} + \text{Cost of college} = 108,000 \, \text{USD} + 30,000 \, \text{USD} = 138,000 \, \text{USD} \][/tex]
### 3. Determining Additional Income per Year after Graduating
This is the difference between their new salary and their previous salary.
- Person A:
[tex]\[ \text{Additional income} = \text{New salary} - \text{Old salary} = 33,000 \, \text{USD/year} - 18,000 \, \text{USD/year} = 15,000 \, \text{USD/year} \][/tex]
- Person B:
[tex]\[ \text{Additional income} = \text{New salary} - \text{Old salary} = 37,000 \, \text{USD/year} - 27,000 \, \text{USD/year} = 10,000 \, \text{USD/year} \][/tex]
### 4. Calculating the Time to Recover the Investment
This is the total investment divided by the additional income per year.
- Person A:
[tex]\[ \text{Time to recover investment} = \frac{99,000 \, \text{USD}}{15,000 \, \text{USD/year}} = 6.6 \, \text{years} \][/tex]
- Person B:
[tex]\[ \text{Time to recover investment} = \frac{138,000 \, \text{USD}}{10,000 \, \text{USD/year}} = 13.8 \, \text{years} \][/tex]
### Conclusion
Person A recovers their investment in 6.6 years, whereas Person B takes 13.8 years to recover their investment. Therefore, Person A recovers their investment in a shorter amount of time.
The correct answer is:
a. Person A recovers their investment in a shorter amount of time.
