You have just finished your year at Queen's. You are debating between pursuing a career as a

commodities trader on Bay Street or as a Finance professor. You project that if you become a

trader your starting salary will be $$50,000$ and it will increase at a $10\%$ rate each year. Every two

years you also expect to earn a bonus of $$150,000.$ However, because of the stress involved in

trading you anticipate retiring after $20$ years and you assign a $20\%$ discount rate to these earnings.

In contrast, if you become a Finance professor, you will have to endure $6$ years of graduate school

during which you will have to borrow $$15,000$ a year $(3\%$ borrowing cost each year$).$ Because of

the less stressful life of a professor, after you complete grad school you except to work as a

professor for $30$ years and assign a $3\%$ discount rate to all earnings involved. If you expect your

salary as a professor to grow at a $1\%$ rate each year, and assuming all cash flows occur at the end

of each year, what starting salary would you have to earn as a professor to make you choose to be

a professor over being a trader? Please round to at least $4$ decimal points for the calculation process

and $2$ decimal points for your final answer. $(12$ marks$)$