Two people quit work and begin college at the same time. Their salary and education information is given in the table below.
| | Salary prior to school | Years attending college | Total cost of college | Salary upon graduating |
| -------- | ----------------------- | ----------------------- | ----------------------- | ---------------------- |
| Person A | $18,000 | 3 | $45000 | $33,000 |
| Person B | $27,000 | 4 | $30,000 | $37,000 |
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.
Answer (2)
Calculate Person A's total investment: I A = 45000 + ( 18000 × 3 ) = 99000 .
Calculate Person B's total investment: I B = 30000 + ( 27000 × 4 ) = 138000 .
Calculate Person A's time to recover investment: T A = 33000 − 18000 99000 = 6.6 years.
Calculate Person B's time to recover investment: T B = 37000 − 27000 138000 = 13.8 years. Person A recovers their investment in a shorter amount of time: P erso n A
Explanation
Understanding the Problem We are given the salary and education information for two people, Person A and Person B, who quit work and begin college at the same time. We need to determine who recovers their investment in a shorter amount of time.
Calculating Person A's Total Investment First, we calculate the total investment for Person A. This includes the cost of college and the lost salary during the years attending college.
The cost of college for Person A is $45,000, and their salary prior to school was $18,000. They attended college for 3 years. Therefore, the total investment for Person A, denoted as I A , is calculated as: I A = 45000 + ( 18000 × 3 ) = 45000 + 54000 = 99000 So, $I_A = $99,000.
Calculating Person B's Total Investment Next, we calculate the total investment for Person B. The cost of college for Person B is $30,000, and their salary prior to school was $27,000. They attended college for 4 years. Therefore, the total investment for Person B, denoted as I B , is calculated as: I B = 30000 + ( 27000 × 4 ) = 30000 + 108000 = 138000 So, $I_B = $138,000.
Calculating Person A's Annual Salary Increase Now, we calculate the annual salary increase for Person A. Their salary upon graduating was $33,000, and their salary prior to school was $18,000. Therefore, the annual salary increase for Person A, denoted as S A , is calculated as: S A = 33000 − 18000 = 15000 So, $S_A = $15,000.
Calculating Person B's Annual Salary Increase We calculate the annual salary increase for Person B. Their salary upon graduating was $37,000, and their salary prior to school was $27,000. Therefore, the annual salary increase for Person B, denoted as S B , is calculated as: S B = 37000 − 27000 = 10000 So, $S_B = $10,000.
Calculating Person A's Time to Recover Investment Next, we calculate the time to recover the investment for Person A. This is the total investment divided by the annual salary increase. Therefore, the time to recover the investment for Person A, denoted as T A , is calculated as: T A = S A I A = 15000 99000 = 6.6 So, T A = 6.6 years.
Calculating Person B's Time to Recover Investment We calculate the time to recover the investment for Person B. This is the total investment divided by the annual salary increase. Therefore, the time to recover the investment for Person B, denoted as T B , is calculated as: T B = S B I B = 10000 138000 = 13.8 So, T B = 13.8 years.
Comparing Recovery Times and Conclusion Finally, we compare T A and T B . Since 6.6 < 13.8 , Person A recovers their investment in a shorter amount of time.
Therefore, the true statement is: Person A recovers their investment in a shorter amount of time.
Examples
Understanding how to calculate the return on investment (ROI) for education is crucial in making informed decisions about college. For instance, consider two different degree programs: one with a shorter duration but lower starting salary, and another with a longer duration but higher starting salary. By calculating the total cost (tuition plus lost wages) and comparing it to the increased earning potential, students can determine which program offers a quicker return on their investment. This analysis helps in prioritizing educational paths that align with financial goals and career aspirations, ensuring a strategic approach to higher education.
Person A recovers their investment in 6.6 years, while Person B takes 13.8 years. Thus, Person A has a quicker recovery time. The correct choice is option a.
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