Your client is 30 years old; and she wants to begin saving for retirement, with the first payment starting from the beginning of next month. She can save up to $12,000 per year by contributing to her retirement plan with monthly payments. Your advice is to invest in a well diversified fund that follows closely the S&P500, which you expect to provide an average return of 8% in the future.

a. If she follows your advice, how much money will she have accumulated on her 64th birthday, the day of her retirement.

b. Suppose your client retires on her 64th birthday. And she wants to start withdrawing $1500 from her retirement account every end of month. Assume that her investment account now earns a more conservative interest of 4% on average. In how many years will she have depleted her account?