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 recovery time: T A = 15000 99000 = 6.6
Calculate Person B's recovery time: T B = 10000 138000 = 13.8 . Person A recovers their investment faster: P erso n A
Explanation
Problem Analysis Let's analyze the problem. We need to determine who recovers their investment faster, Person A or Person B. To do this, we'll calculate the total investment for each person (college costs plus lost salary during college) and then divide that by their annual salary increase after graduating.
Calculating Person A's Total Investment First, we calculate the total investment for Person A. This is the sum of their college costs and the salary they would have earned if they hadn't gone to college. So, for Person A:
Total Investment (Person A) = Cost of College + (Salary Prior to School × Years Attending College)
I A = 45000 + ( 18000 × 3 ) = 45000 + 54000 = 99000
So, Person A's total investment is $99,000.
Calculating Person B's Total Investment Next, we calculate the total investment for Person B using the same method:
Total Investment (Person B) = Cost of College + (Salary Prior to School × Years Attending College)
I B = 30000 + ( 27000 × 4 ) = 30000 + 108000 = 138000
Person B's total investment is $138,000.
Calculating Person A's Annual Salary Increase Now, we need to calculate the annual salary increase for each person. This is the difference between their salary upon graduating and their salary prior to school.
For Person A:
Annual Salary Increase (Person A) = Salary Upon Graduating - Salary Prior to School
S A = 33000 − 18000 = 15000
Person A's annual salary increase is $15,000.
Calculating Person B's Annual Salary Increase Similarly, for Person B:
Annual Salary Increase (Person B) = Salary Upon Graduating - Salary Prior to School
S B = 37000 − 27000 = 10000
Person B's annual salary increase is $10,000.
Calculating Person A's Recovery Time Now, we calculate the time it takes for each person to recover their investment. This is the total investment divided by the annual salary increase.
For Person A:
Time to Recover Investment (Person A) = Total Investment / Annual Salary Increase
T A = 15000 99000 = 6.6
Person A recovers their investment in 6.6 years.
Calculating Person B's Recovery Time For Person B:
Time to Recover Investment (Person B) = Total Investment / Annual Salary Increase
T B = 10000 138000 = 13.8
Person B recovers their investment in 13.8 years.
Comparing Recovery Times and Concluding Comparing the recovery times, we see that Person A recovers their investment in 6.6 years, while Person B recovers their investment in 13.8 years. Therefore, Person A recovers their investment in a shorter amount of time.
Examples
This type of calculation is useful when deciding whether to invest in further education or training. By comparing the costs (tuition, fees, and foregone salary) with the expected increase in future earnings, one can estimate the payback period and make an informed decision about the financial viability of the investment. For example, a software engineer might consider whether a specialized certification is worth the cost by estimating how much their salary will increase and how long it will take to recoup the investment in the certification program. This helps in making informed career and financial decisions.
Person A has a total investment of $99,000 and recovers it in 6.6 years, while Person B has a total investment of $138,000 and takes 13.8 years to recover. This means Person A recovers their investment faster. The correct option is A.
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