Congratulations on completing your college education! You are now faced with a tough decision between pursuing a career in banking or becoming a Finance Professor. If you decide to become a banker, you can start your job immediately, with a yearly salary of $$50,000$ for the first two years. Your salary will increase to $$60,000$ in the third year, and then grow at a rate of $5\%$ each year thereafter. You anticipate working for $30$ years before retiring. However, given the uncertainty of the banking industry, you have decided to use a $10\%$ discount rate to evaluate your potential earnings.

On the other hand, if you choose to become a Finance Professor, you'll need to pursue six more years of graduate studies. Your tuition and other expenses will amount to $$18,000$ per year, with the first payment due today. After completing your graduate studies, it will take you two more years to find a job as a Professor, so you'll start earning a salary at the end of year $8.$ You expect to work for $40$ years as a Professor, with a starting salary of $$55,000,$ which will increase by $3\%$ each year. Given the relative stability of academia, you've decided to use a $5\%$ discount rate to evaluate your potential earnings.