To find out which person recovers their college investment in a shorter amount of time, we need to compute and compare the time it takes for each person to recover the cost of college from their increased salary after graduation.
For Person A:
1. Salary prior to school: \[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
The increase in salary after graduation compared to before is:
\[
\text{Additional income for Person A} = \text{Salary upon graduating} - \text{Salary prior to school} = 33,000 - 18,000 = \$[/tex]15,000 \text{ per year}
\]
The time to recover the cost of college is:
[tex]\[
\text{Time to recover for Person A} = \frac{\text{Total cost of college}}{\text{Additional income}} = \frac{45,000}{15,000} = 3 \text{ years}
\][/tex]
For Person B:
1. Salary prior to school: \[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
The increase in salary after graduation compared to before is:
\[
\text{Additional income for Person B} = \text{Salary upon graduating} - \text{Salary prior to school} = 37,000 - 27,000 = \$[/tex]10,000 \text{ per year}
\]
The time to recover the cost of college is:
[tex]\[
\text{Time to recover for Person B} = \frac{\text{Total cost of college}}{\text{Additional income}} = \frac{30,000}{10,000} = 3 \text{ years}
\][/tex]
Both persons take the same amount of time (3 years) to recover their college investment from their increased salary.
Therefore, the correct answer is:
c. They recover their investments in the same amount of time.
