t is Jan $1$st$,2023,$ Herald just turned $18$ years old and has recently been admitted to two programs: B$.$S$.$ in chemical engineering and B$.$A$.$ in business administration. Both programs take $4$ years to complete. Herald is also considering working with his uncle in home renovation. Upon graduation from either of the university programs, he$$ll start earning $$70,000$ per year paid at the end of the year. If he pursues the engineering degree, he will have to pay $$20,000$ at the beginning of each year as tuition until graduation $(4$ installments$),$ and his salary would increase by $2\%$ per year until retirement. The tuition of the business program is slightly higher at $$25,000$ each year $($paid at the beginning of the year$).$ However, if he graduates with B$.$A$.$ in business, his salary doesn$$t grow for $5$ years, but starting from the sixth year, his salary grows by $4\%$ per year till retirement as he plans to assume a managerial position after $5$ years. Finally, if he works with his uncle, his starting salary is $$40,000$ unchanged until retirement. Assuming the retirement age of $65$ and a valuation rate of $6\%$ calculate the PV of each career choice and give him financial advice about the best career path.