A CUHK$($SZ$)$ graduate earns $150K$ per year starting from the age of $23,$ growing at $4\%$ per year. The annual expenditure is $100K$ 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 $150k$ per year. After graduation, the starting salary will be $200K$ 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?