4. In the setting of problem 3(a), John will transfer her money at the age of 65 (his retirement) from his 4011': account (valued at $1.5 million) into a safe account which will earn an annual interest of 3.6% (APR on a monthly base). (a) If he wants to use up all his money at the age of 85, how much can he spend each month after retirement? (b) If John expects to die at the age of 95 and use up all his money: how much less can he spend each month after retirement? (c) Suppose there is T096 change that John will live up to 85 and 30% he will live up to 95. If John wants to buy an annuity product from an investment bank: how much will he get each month? (hint: In an ideal case: suppose the investment bank does not charge a fee. In this case, you can get the expected payment and the bank will earn the interest on balance.) What is the equivalent annuity factor?r (that is if you want to get $1 each month until you die, how much do you need now?) (d) If John only spend $6000 (Le. 4% of his balance) each month: and he dies at the age of 90, how much he could pass to his children if he does not buy the annuity product