Answer :
Let's break down the problem to determine how long it takes each person to recover their investment in education.
### Person A:
1. Salary prior to school: \[tex]$18,000 2. Years attending college: 3 3. Total cost of college: \$[/tex]45,000
4. Salary upon graduating: \[tex]$33,000 Step-by-Step Calculation for Person A: 1. Loss of income during college: \[ 18,000 \, \text{USD/year} \times 3 \, \text{years} = 54,000 \, \text{USD} \] 2. Total investment (cost of college + loss of income): \[ 54,000 \, \text{USD (loss of income)} + 45,000 \, \text{USD (cost of college)} = 99,000 \, \text{USD} \] 3. Extra annual income after graduating: \[ 33,000 \, \text{USD} - 18,000 \, \text{USD} = 15,000 \, \text{USD} \] 4. Years to recover the investment: \[ \frac{99,000 \, \text{USD}}{15,000 \, \text{USD/year}} = 6.6 \, \text{years} \] ### Person B: 1. Salary prior to school: \$[/tex]27,000
2. Years attending college: 4
3. Total cost of college: \[tex]$30,000 4. Salary upon graduating: \$[/tex]37,000
Step-by-Step Calculation for Person B:
1. Loss of income during college:
[tex]\[ 27,000 \, \text{USD/year} \times 4 \, \text{years} = 108,000 \, \text{USD} \][/tex]
2. Total investment (cost of college + loss of income):
[tex]\[ 108,000 \, \text{USD (loss of income)} + 30,000 \, \text{USD (cost of college)} = 138,000 \, \text{USD} \][/tex]
3. Extra annual income after graduating:
[tex]\[ 37,000 \, \text{USD} - 27,000 \, \text{USD} = 10,000 \, \text{USD} \][/tex]
4. Years to recover the investment:
[tex]\[ \frac{138,000 \, \text{USD}}{10,000 \, \text{USD/year}} = 13.8 \, \text{years} \][/tex]
### Conclusion:
Comparing the recovery times:
- Person A needs 6.6 years to recover their investment.
- Person B needs 13.8 years to recover their investment.
Therefore, Person A recovers their investment in a shorter amount of time. Thus, the correct answer is:
a. Person A recovers their investment in a shorter amount of time.
### Person A:
1. Salary prior to school: \[tex]$18,000 2. Years attending college: 3 3. Total cost of college: \$[/tex]45,000
4. Salary upon graduating: \[tex]$33,000 Step-by-Step Calculation for Person A: 1. Loss of income during college: \[ 18,000 \, \text{USD/year} \times 3 \, \text{years} = 54,000 \, \text{USD} \] 2. Total investment (cost of college + loss of income): \[ 54,000 \, \text{USD (loss of income)} + 45,000 \, \text{USD (cost of college)} = 99,000 \, \text{USD} \] 3. Extra annual income after graduating: \[ 33,000 \, \text{USD} - 18,000 \, \text{USD} = 15,000 \, \text{USD} \] 4. Years to recover the investment: \[ \frac{99,000 \, \text{USD}}{15,000 \, \text{USD/year}} = 6.6 \, \text{years} \] ### Person B: 1. Salary prior to school: \$[/tex]27,000
2. Years attending college: 4
3. Total cost of college: \[tex]$30,000 4. Salary upon graduating: \$[/tex]37,000
Step-by-Step Calculation for Person B:
1. Loss of income during college:
[tex]\[ 27,000 \, \text{USD/year} \times 4 \, \text{years} = 108,000 \, \text{USD} \][/tex]
2. Total investment (cost of college + loss of income):
[tex]\[ 108,000 \, \text{USD (loss of income)} + 30,000 \, \text{USD (cost of college)} = 138,000 \, \text{USD} \][/tex]
3. Extra annual income after graduating:
[tex]\[ 37,000 \, \text{USD} - 27,000 \, \text{USD} = 10,000 \, \text{USD} \][/tex]
4. Years to recover the investment:
[tex]\[ \frac{138,000 \, \text{USD}}{10,000 \, \text{USD/year}} = 13.8 \, \text{years} \][/tex]
### Conclusion:
Comparing the recovery times:
- Person A needs 6.6 years to recover their investment.
- Person B needs 13.8 years to recover their investment.
Therefore, Person A recovers their investment in a shorter amount of time. Thus, the correct answer is:
a. Person A recovers their investment in a shorter amount of time.
