You have just finished your undergraduate degree and you have two career options:

Option $1$: Accepting a job offer with the starting salary of $$6,300$ per month $($paid at the end of

the month$).$ You will work in this company for $35$ years.

Option $2$: Choosing a graduate program which will cost you $$35,000$ per year for the next two

years $($paid at the beginning of each year$).$ Following the graduate school, you can get a job that

offers the initial salary of $$7,500$ per month $($first one paid at the end of month $25).$ You will work

in this company for $33$ years

a$.$If the annual discount rate is $5\mathrm{.}40\%,$ which career option is more lucrative for you?

b$.$At what annual tuition will you be indifferent between these two career options?

c$.$ If the lower NPV option comes with a signing bonus $($paid at the end of month $24),$ at

what signing bonus will you be indifferent?