Following graduation with a B$.$S$.$ in computer science, Billy faces a dilemma. He had no internship or experience during college, and most full$-$time $$entry$-$level$$ jobs in his desired field expect at least two years of experience or a Master$$s degree. To continue in his career, he can either pay to attend a Master$$s program or work for NoviceCo, a company that hires and trains people with no experience. The cost of a Master$$s degree is $$52,000$ per year and it takes $2$ years to complete the degree. Tuition is paid each year before classes begin, while earnings are received at the end of the year. If he chooses to work for NoviceCo, he will earn $$20,000$ per year and receive extensive training, but he promises to continue at this rate for $4$ years, otherwise he must pay a massive penalty $($such that it never pays off to leave the company early$).$ Upon completion of either educational path, Billy would be able to earn $$100,000$ each year for the rest of his life. He is currently $22$ years old, and plans to work until age $62.$ a$.$ Assume Billy can borrow and lend at a rate of $5\%.$ If he would like to maximize his lifetime earnings, which path will he choose and why?