A CUHK$($SZ$)$ graduate earns $150$K per year starting from the age of $23,$ growing at $4\%$ per year. The

annual expenditure is $100$K in the first year, growing at $2\%$ per year. Suppose all the cash flow occurs at

the birthdays, starting at age $23.$ The investment return per year is $7\%.$

$(1)$ How much would $($s$)$he have in the bank account at retirement at age $60?$

$(2)$ The student receives an offer from SFI and is trying to decide whether to take this offer. The master

program takes $2$ years, and costs $150$k per year. After graduation, the starting salary will be $200$K per

year, also growing at $4\%$ per year. Assume the living expenditures do not change. What is the NPV of

getting a master$$s degree?