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.
Please select the best answer from the choices provided
Answer (1)
Calculate the lost income during college for both Person A and Person B.
Determine the total investment for each person by adding their lost income and the total cost of college.
Calculate the increased salary after graduation for both Person A and Person B.
Compute the time to recover the investment for each person and compare the results to find who recovers faster. Person A recovers their investment in a shorter amount of time: 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 time it takes for each person to recover their investment, considering their lost income during college, the cost of college, and their increased salary after graduation.
Calculating Lost Income First, we calculate the lost income for Person A during their 3 years of college: L os t I n co m e A = S a l a ry P r i or t o S c h oo l A × Y e a rs A tt e n d in g C o ll e g e A = $18 , 000 × 3 = $54 , 000 Next, we calculate the lost income for Person B during their 4 years of college: L os t I n co m e B = S a l a ry P r i or t o S c h oo l B × Y e a rs A tt e n d in g C o ll e g e B = $27 , 000 × 4 = $108 , 000
Calculating Total Investment Now, we calculate the total investment for Person A, which includes the lost income and the cost of college: T o t a l I n v es t m e n t A = L os t I n co m e A + T o t a l C os t o f C o ll e g e A = $54 , 000 + $45 , 000 = $99 , 000 Similarly, we calculate the total investment for Person B: T o t a l I n v es t m e n t B = L os t I n co m e B + T o t a l C os t o f C o ll e g e B = $108 , 000 + $30 , 000 = $138 , 000
Calculating Increased Salary Next, we determine the increase in salary after graduation for Person A: I n cre a se d S a l a r y A = S a l a ry U p o n G r a d u a t in g A − S a l a ry P r i or t o S c h oo l A = $33 , 000 − $18 , 000 = $15 , 000 And for Person B: I n cre a se d S a l a r y B = S a l a ry U p o n G r a d u a t in g B − S a l a ry P r i or t o S c h oo l B = $37 , 000 − $27 , 000 = $10 , 000
Calculating Recovery Time Now, we calculate the time it takes for Person A to recover their investment: T im e t o R eco v e r A = I n cre a se d S a l a r y A T o t a l I n v es t m e n t A = $15 , 000 $99 , 000 = 6.6 ye a rs And for Person B: T im e t o R eco v e r B = I n cre a se d S a l a r y B T o t a l I n v es t m e n t B = $10 , 000 $138 , 000 = 13.8 ye a rs
Comparing Recovery Times and Conclusion Comparing the recovery times, Person A recovers their investment in 6.6 years, while Person B takes 13.8 years. Therefore, Person A recovers their investment in a shorter amount of time.
Examples
Understanding the return on investment (ROI) for education is crucial in making informed career decisions. For instance, consider a student deciding between a shorter, less expensive program and a longer, more costly one. By calculating the lost income during studies, the total cost of education, and the potential increase in salary after graduation, the student can estimate how long it will take to recoup their investment. This analysis helps in choosing the program that offers a quicker financial recovery and better long-term financial benefits, ensuring a more strategic approach to education and career planning.
