Your financial planner has advised you to initiate a retirement account while you are still young. Today is your 35th birthday and you are planning to retire at age 65. Actuarial tables show that individuals in your age/demographic group have a life expentancy of 75. You would like to begin paying yourself a cash annuity beginning on your 66th birthday, starting at $50,000 but increasing by 4% per year up until death. (You may assume that the actuarial table provides a precise estimate of your longevity).

1. What amount must you deposit at the end of each year through age 65 at an interest/discount rate of 8% compounded annually to fund your retirement account? (Hint: It helps to look at this problem at two points at time both when youre 65 and now).
2. How would you answer the last question if the rate were 9% rather than 8%?
3. After you have paid your last installment on your 65th birthday, you learn that a revolutionary discovery in medical science has increased your life expectancy to 85 rather than 75. Assuming you still want to pay yourself an annuity that grows at 4% per year, what is the baseyear annuity payment that you can afford, under the 9% discount rate from the previous question