An engineer graduates at age 22, and she gets a job that pays $65,000 per year. She wants to invest.

An engineer graduates at age 22, and she gets a job that pays $65,000 per year. She wants to invest enough to fund her own retirement without relying on an employer pension program or Social Security. Her goal is to have $1.5 million saved for retirement at age 67. She is relatively confident that her investments will earn an average interest rate of at least 4% per year.

(a) Assume that she makes equal annual deposits starting on her 23^{rd} birthday and continuing through her 67th birthday. How much must she invest each year to meet her goal?

(b) Suppose she invests the same amount from part (a) every year starting on her 33rd birthday. How much money will she have in the account on her 67th birthday under this scenario?