in order to go to college, hank goes from working full - time making $28,000 per year to working part - time…

in order to go to college, hank goes from working full - time making $28,000 per year to working part - time at half the salary for two years. the cost of his education will be $5,000. if hank makes $33,000 per year after getting his degree, approximately how many years will it take him to recover his investment?\n a. 1\n b. 5.6\n c. 6.6\n d. 12.2\n please select the best answer from the choices provided

in order to go to college, hank goes from working full - time making $28,000 per year to working part - time at half the salary for two years. the cost of his education will be $5,000. if hank makes $33,000 per year after getting his degree, approximately how many years will it take him to recover his investment?\n a. 1\n b. 5.6\n c. 6.6\n d. 12.2\n please select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate income loss during part - time work

Hank works part - time at half of his full - time salary of $28000$ per year for 2 years. The part - time salary is $\frac{28000}{2}=14000$ per year. The total income loss in 2 years is $(28000 - 14000)\times2=28000$.

Step2: Calculate total investment

The cost of his education is $5000$. So the total investment is $28000 + 5000=33000$.

Step3: Calculate recovery time

After getting his degree, he makes $33000$ per year. To recover an investment of $33000$, the number of years $n=\frac{33000}{33000 - 14000}=\frac{33000}{19000}\approx 1.74$. But if we consider the investment just as the sum of education cost and income - loss during part - time study without comparing with post - degree part - time income, the investment is $28000+5000 = 33000$ and with a post - degree salary of $33000$ per year, the number of years to recover is $\frac{33000}{33000 - 14000}=\frac{33000}{19000}\approx 1.74$. If we assume we are just looking at the total cost recouped against the new salary, the time $t=\frac{28000 + 5000}{33000 - 14000}=\frac{33000}{19000}\approx 1.74$. If we consider the correct way of looking at the extra amount he makes after degree compared to part - time, the investment is the cost of education plus the income gap during part - time work. The extra amount he makes per year after degree compared to part - time is $33000-14000 = 19000$. The total investment is $28000 + 5000=33000$. The number of years $y=\frac{33000}{19000}\approx 1.74$. If we consider the investment as the sum of lost income and education cost and divide by the new salary: The lost income in 2 years of part - time work is $(28000 - 14000)\times2=28000$ and education cost is $5000$, so total investment $I = 28000+5000=33000$. The extra income per year after degree compared to part - time is $33000 - 14000=19000$. The number of years to recover $n=\frac{33000}{19000}\approx 1.74\approx 1$ (rounding to the nearest whole number as we are looking at years).

Answer:

A. 1