Two people quit work and begin college at the same time. Their salary and education information is given in the table below.

\begin{tabular}{|c|c|c|c|c|}
\hline
& \begin{tabular}{c}
Salary prior to \\
school
\end{tabular} & \begin{tabular}{c}
Years attending \\
college
\end{tabular} & Total cost of college & \begin{tabular}{c}
Salary upon \\
graduating
\end{tabular} \\
\hline
Person A & [tex]$\$[/tex] 18,000[tex]$ & 3 & $[/tex]\[tex]$ 45,000$[/tex] & [tex]$\$[/tex] 33,000$ \\
\hline
Person B & [tex]$\$[/tex] 27,000[tex]$ & 4 & $[/tex]\[tex]$ 30,000$[/tex] & [tex]$\$[/tex] 37,000$ \\
\hline
\end{tabular}

Choose the true statement.

A. Person A recovers their investment in a shorter amount of time.
B. Person B recovers their investment in a shorter amount of time.
C. They recover their investments in the same amount of time.
D. There is too little information to compare the time to recover their investments.

Please select the best answer from the choices provided.



Answer :

Let's solve the problem step-by-step.

1. Opportunity Cost Calculation:
- Person A:
- Salary prior to school: $18,000
- Years attending college: 3
- Opportunity cost = Salary prior to school Years attending college
- \( \text{Opportunity cost for Person A} = 18,000 \times 3 = 54,000 \)

- Person B:
- Salary prior to school: $27,000
- Years attending college: 4
- Opportunity cost = Salary prior to school
Years attending college
- \( \text{Opportunity cost for Person B} = 27,000 \times 4 = 108,000 \)

2. Total Investment Calculation:
- Person A:
- Opportunity cost: $54,000
- Total cost of college: $45,000
- Total investment = Opportunity cost + Total cost of college
- \( \text{Total investment for Person A} = 54,000 + 45,000 = 99,000 \)

- Person B:
- Opportunity cost: $108,000
- Total cost of college: $30,000
- Total investment = Opportunity cost + Total cost of college
- \( \text{Total investment for Person B} = 108,000 + 30,000 = 138,000 \)

3. Time to Recover the Investment Calculation:
- Person A:
- Total investment: $99,000
- Salary upon graduating: $33,000
- Salary prior to school: $18,000
- Increment in salary: [tex]$33,000 - $[/tex]18,000 = $15,000
- Time to recover investment = Total investment / Increment in salary
- \( \text{Time to recover for Person A} = \frac{99,000}{15,000} = 6.6 \) years

- Person B:
- Total investment: $138,000
- Salary upon graduating: $37,000
- Salary prior to school: $27,000
- Increment in salary: [tex]$37,000 - $[/tex]27,000 = $10,000
- Time to recover investment = Total investment / Increment in salary
- \( \text{Time to recover for Person B} = \frac{138,000}{10,000} = 13.8 \) years

Based on the calculations above:
- Person A recovers their investment in 6.6 years.
- Person B recovers their investment in 13.8 years.

Therefore, the true statement is:
a. Person A recovers their investment in a shorter amount of time.