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$$ follows:$$

bullet If you take the$$ "get a$$ job" route, you expect to start off with a salary of $$$$45$ comma $000$ per year. There is no way to predict what will happen in the$$ future, but your best guess is that your salary will grow at $4$ percent per year until you retire in $44$ years.

bullet 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 $$$$80$ comma $000$ per year.$$ Moreover, you expect your salary to grow by $7$ percent per year until you retire $37$ 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 $$$$140$ comma $000$ in lost income over the $3$ years of law$$ school: $$$$45$ comma $000$ the first$$ year, $ $46$ comma $800$ the second$$ year, and $$$$48$ comma $672$ the third year.

a$.$ To start your analysis of whether to go to law$$ school, calculate the present value of the future earnings that you will realize by going directly to$$ work, assume a discount rate of $5$ percent.

b$.$ What is the present value today of your future earnings if you decide to attend law$$ school, assuming a discount rate of $5$percent$?$ Remember that you will be in law school for $3$ years before you start to work as a lawyer. $($Hint$$: assume that you are paid at the end of each$$ year, so that your first salary payment if you decide to go to law school occurs $4$ years from$$ now.$)$

c$.$ If you pay your law school tuition at the beginning of each$$ year, what is the present value of your$$ tuition, assuming a discount rate of $5$percent$?$

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Part $1$

a$.$ What is the present value of the future earnings that you will realize by going directly to$$ work, assuming a discount rate of $5$percent$?$