Your retirement account (which is expected to yield an 8% return per year) has a current balance of $5,000. You are going to retire in 20 years.

a. How much would you need to invest each year in order to accumulate a total amount that will guarantee withdrawing $10,000 annually for 30 years starting from year 21 ?

b. If you decide to invest monthly, how much would you need to invest each month in order to accumulate a total amount that will guarantee withdrawing $10,000 annually for 30 years starting from year 21?

c. Compare the annual investments in part (a) with the total amount that you would invest in one year in part (b) (12 times the monthly investments). Which one is greater? Why?

d. You are worried about future inflations and wondering what your answer to part a would be if you plan increasing withdrawals; $10,000 at the end of year 21 growing at a constant rate of 4% each year for 30 years.