$($Comprehensive Problem$)$Suppose that you are in the fall of your senior year and are faced with the choice of either getting a job when you graduate or going to law school. Of$$ course, your choice is not purely financial. $$ However, to make an informed decision you would like to know the financial implications of the two alternatives. $$ Let's assume that your alternatives are as$$ follows:$$

If you take the$$ "get a$$ job" route you expect to start off with a salary of $$$$40$ comma $000$

per year. There is no way to predict what will happen in the$$ future, your best guess is that your salary will grow at $4$

percent per year until you retire in $42$

years. As a law$$ student, you will be paying $$$$30$ comma $000$

per year tuition for each of the $3$

years you are in graduate school. $$ However, you can then expect a job with a starting salary of $$$$70$ comma $000$

per year. $$ Moreover, you expect your salary to grow by $8$

percent per year until you retire $36$

years later.$$

$$Clearly$,$ your total expected lifetime salary will be higher if you become a lawyer. $$ However, the additional future salary is not free. You will be paying $$$$30$ comma $000$

in tuition at the beginning of each of the $3$

years of law school. In$$ addition, you will be giving up a little more than $$$$124$ comma $000$

in lost income over the three years of law$$ school:$$$$40$ comma $000$

the first$$ year, $ $41$ comma $600$

the second$$ year, and $$$$43$ comma $264$

the third year.