the future, but your best guess is that your salary will grow at $5$ percent per year until you retire in $45$ years.

As a law student, you will be paying $$20,000$ per year tuition for each of the $3$ years you are in graduate school. However, you can then expect a job with a starting salary of $$70,000$ per year. Moreover, you expect your salary to grow by $8$ percent per year until you retire $38$ 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 $$20,000$ in tuition at the beginning of each of the $3$ years of law school. In addition, you will be giving up a little more than $$141,000$ in lost income over the $3$ years of law school: $$45,000$ the first year, $$47,250$ the second year, and $$49,613$ the third year.

a$.$ To start your analysis of whether to go to law school, calculate the present value of the futare earnings that you will realize by going directly to work, assume a discount rate of $6$ percent.

b$.$ What is the present value today of your future earnings if you decide to attend law school, assuming a discount rate of $6$ 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 $6$ nercent?

a$.$ What is the present value of the future earnings that you will realize by going directly to work, assuming a discount rate of $6$ percent?

$ $($Round to the nearest cent.$)$

b$.$ What is the present value today of your future earnings if you decide to attend law school, assuming a discount rate of $6$ percent?

$ $($Round to the nearest cent.$)$

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 $6$ percent?

$ $($Round to the nearest cent.$)$