You begin saving for retirement at age 22. Denote the end of the year in which you turn 22 as year 1. You save $1000 in the first calendar year and continue saving thru the year you turn age 33. You increase the amount you save each year by $500 so that in the year you are age 33 you save $6500. You do not continue saving when you are 34 or older. Assume that savings are invested at the end of each calendar year. Assume that during your working life you earn a return of 8% per year, and that when you retire at age 65 you move your assets into more conservative investments and earn a return of 3% per year.
(a) Compute the amount of your savings at the end of the year in which you are age 64.
(b) Compute the annual income you will receive during retirement assuming that you take equal annual payments for 20 years
beginning the year when you turn 65.