Whether you're a student or a professional, IDNLearn.com has answers for everyone. Ask your questions and receive comprehensive, trustworthy responses from our dedicated team of experts.
Sagot :
To determine which person recovers their investment in a shorter amount of time, we need to consider both the direct costs of college and the opportunity cost of lost wages while attending college. Here's a step-by-step breakdown:
1. Person A:
- Salary prior to college: \[tex]$18,000 - Years attending college: 3 - Total cost of college: \$[/tex]45,000
- Salary upon graduating: \[tex]$33,000 2. Person B: - Salary prior to college: \$[/tex]27,000
- Years attending college: 4
- Total cost of college: \[tex]$30,000 - Salary upon graduating: \$[/tex]37,000
Next, let's calculate the total loss in salary for each person while they are in college.
Person A's loss of salary during college:
[tex]\[ \text{Loss Salary}_A = \text{Years Attending College}_A \times \text{Salary Prior}_A \][/tex]
[tex]\[ \text{Loss Salary}_A = 3 \times 18,000 \][/tex]
[tex]\[ \text{Loss Salary}_A = \$54,000 \][/tex]
Person B's loss of salary during college:
[tex]\[ \text{Loss Salary}_B = \text{Years Attending College}_B \times \text{Salary Prior}_B \][/tex]
[tex]\[ \text{Loss Salary}_B = 4 \times 27,000 \][/tex]
[tex]\[ \text{Loss Salary}_B = \$108,000 \][/tex]
Now, we sum the total cost of college and the loss of salary to find each person’s total investment.
Person A's total investment:
[tex]\[ \text{Total Investment}_A = \text{Loss Salary}_A + \text{Total Cost of College}_A \][/tex]
[tex]\[ \text{Total Investment}_A = 54,000 + 45,000 \][/tex]
[tex]\[ \text{Total Investment}_A = \$99,000 \][/tex]
Person B's total investment:
[tex]\[ \text{Total Investment}_B = \text{Loss Salary}_B + \text{Total Cost of College}_B \][/tex]
[tex]\[ \text{Total Investment}_B = 108,000 + 30,000 \][/tex]
[tex]\[ \text{Total Investment}_B = \$138,000 \][/tex]
To find out the time it takes for each person to recover their investment, we divide their total investment by their post-graduation salary.
Person A's recovery time:
[tex]\[ \text{Recovery Time}_A = \frac{\text{Total Investment}_A}{\text{Salary Upon Graduating}_A} \][/tex]
[tex]\[ \text{Recovery Time}_A = \frac{99,000}{33,000} \][/tex]
[tex]\[ \text{Recovery Time}_A = 3 \text{ years} \][/tex]
Person B's recovery time:
[tex]\[ \text{Recovery Time}_B = \frac{\text{Total Investment}_B}{\text{Salary Upon Graduating}_B} \][/tex]
[tex]\[ \text{Recovery Time}_B = \frac{138,000}{37,000} \][/tex]
[tex]\[ \text{Recovery Time}_B \approx 3.73 \text{ years} \][/tex]
Comparing the recovery times:
- Person A recovers their investment in approximately 3 years.
- Person B recovers their investment in approximately 3.73 years.
Therefore, the best answer is:
a. Person A recovers their investment in a shorter amount of time.
1. Person A:
- Salary prior to college: \[tex]$18,000 - Years attending college: 3 - Total cost of college: \$[/tex]45,000
- Salary upon graduating: \[tex]$33,000 2. Person B: - Salary prior to college: \$[/tex]27,000
- Years attending college: 4
- Total cost of college: \[tex]$30,000 - Salary upon graduating: \$[/tex]37,000
Next, let's calculate the total loss in salary for each person while they are in college.
Person A's loss of salary during college:
[tex]\[ \text{Loss Salary}_A = \text{Years Attending College}_A \times \text{Salary Prior}_A \][/tex]
[tex]\[ \text{Loss Salary}_A = 3 \times 18,000 \][/tex]
[tex]\[ \text{Loss Salary}_A = \$54,000 \][/tex]
Person B's loss of salary during college:
[tex]\[ \text{Loss Salary}_B = \text{Years Attending College}_B \times \text{Salary Prior}_B \][/tex]
[tex]\[ \text{Loss Salary}_B = 4 \times 27,000 \][/tex]
[tex]\[ \text{Loss Salary}_B = \$108,000 \][/tex]
Now, we sum the total cost of college and the loss of salary to find each person’s total investment.
Person A's total investment:
[tex]\[ \text{Total Investment}_A = \text{Loss Salary}_A + \text{Total Cost of College}_A \][/tex]
[tex]\[ \text{Total Investment}_A = 54,000 + 45,000 \][/tex]
[tex]\[ \text{Total Investment}_A = \$99,000 \][/tex]
Person B's total investment:
[tex]\[ \text{Total Investment}_B = \text{Loss Salary}_B + \text{Total Cost of College}_B \][/tex]
[tex]\[ \text{Total Investment}_B = 108,000 + 30,000 \][/tex]
[tex]\[ \text{Total Investment}_B = \$138,000 \][/tex]
To find out the time it takes for each person to recover their investment, we divide their total investment by their post-graduation salary.
Person A's recovery time:
[tex]\[ \text{Recovery Time}_A = \frac{\text{Total Investment}_A}{\text{Salary Upon Graduating}_A} \][/tex]
[tex]\[ \text{Recovery Time}_A = \frac{99,000}{33,000} \][/tex]
[tex]\[ \text{Recovery Time}_A = 3 \text{ years} \][/tex]
Person B's recovery time:
[tex]\[ \text{Recovery Time}_B = \frac{\text{Total Investment}_B}{\text{Salary Upon Graduating}_B} \][/tex]
[tex]\[ \text{Recovery Time}_B = \frac{138,000}{37,000} \][/tex]
[tex]\[ \text{Recovery Time}_B \approx 3.73 \text{ years} \][/tex]
Comparing the recovery times:
- Person A recovers their investment in approximately 3 years.
- Person B recovers their investment in approximately 3.73 years.
Therefore, the best answer is:
a. Person A recovers their investment in a shorter amount of time.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.
