Q 1. Today is John Tardys 45^th birthday and, despite his finance professors advice, he hasnt started to save for retirement. John cant believe time has passed so quickly. John wants to retire on his 65^th birthday; mortality tables indicate his life expectancy is 85. Therefore, he will need a retirement fund that will sustain him for 20 years, or 240 months. John intends to completely deplete this fund by age 85, leaving nothing for his heirs.

a) What amount of money must be in the retirement fund on Johns 65^th birthday if he will withdraw $6,000 then and every subsequent month? John will withdraw the last payment one month before his 85^th birthday for a total of 240 payments. The rate of return on the retirement fund during this period is 9% per year..

b) How much money must John save each month beginning one month from today, his 45^th birthday to accumulate the necessary funds? The rate of return during this period is 10.8% per year.

c) John would like to start saving right now, of course, but his 19-year old daughter is about to start college at an exclusive eastern school and he hasnt saved for her tuition either. Suppose John can pay his daughters expenses out of his current income but cant start saving for his retirement until she graduates (she is almost certain to take five years to finish). How much money must John save each month, beginning one month after his 50^th birthday to accumulate the necessary funds.

d) If John if expecting inflation rate of 3% per year, he expects to get $6000 on the day he retires (on his 65^th birthday) but wants to be compensated for the inflation for each payment one month from his 65^th birthday until age 85. You expect the rate of return to be 9% per year. Please note, he will receive his inflation adjusted money every month until one month before his 85^th birthday.