To determine which person recovers their investment in college in a shorter amount of time, we need to follow these steps:
1. Calculate the lost wages during college for each person:
- Lost wages for Person A over 3 years:
[tex]\[
\text{Lost wages}_A = \$18,000 \times 3 = \$54,000
\][/tex]
- Lost wages for Person B over 4 years:
[tex]\[
\text{Lost wages}_B = \$27,000 \times 4 = \$108,000
\][/tex]
2. Calculate the total investment for each person (lost wages + college cost):
- Total investment for Person A:
[tex]\[
\text{Total investment}_A = \$54,000 + \$45,000 = \$99,000
\][/tex]
- Total investment for Person B:
[tex]\[
\text{Total investment}_B = \$108,000 + \$30,000 = \$138,000
\][/tex]
3. Calculate the annual increase in salary after graduating:
- Annual increase in salary for Person A:
[tex]\[
\text{Annual increase}_A = \$33,000 - \$18,000 = \$15,000
\][/tex]
- Annual increase in salary for Person B:
[tex]\[
\text{Annual increase}_B = \$37,000 - \$27,000 = \$10,000
\][/tex]
4. Calculate the time to recover the investment for each person:
- Time to recover the investment for Person A:
[tex]\[
\text{Time to recover}_A = \frac{\$99,000}{\$15,000} = 6.6 \text{ years}
\][/tex]
- Time to recover the investment for Person B:
[tex]\[
\text{Time to recover}_B = \frac{\$138,000}{\$10,000} = 13.8 \text{ years}
\][/tex]
Since [tex]\(6.6\)[/tex] years (for Person A) is less than [tex]\(13.8\)[/tex] years (for Person B), the true statement is:
a. Person A recovers their investment in a shorter amount of time.
