QUESTION 1 Professor Balducci is currently age 60 and will retire immediately. He purchased a whole life annuity-due contract which will pay him on a monthly basis the following benefits: $12,000 each year for the next 10 years; $24,000 each year for the following 5 years after that; and finally, $48,000 each year thereafter. You are given: i = 5% and the following table: 60 65 70 75 1000A (12) 661.11 712.33 760.65 804.93 5Px 0.8504 0.7926 0.7164 0.6196 Calculate the APV of Professor Balducci's life annuity benefits. QUESTION 2 For a whole life annuity-due of $1,000 per year on (65), you are given: Mortality follows Gompertz law with Mx = Bc", for x 20, where B = 5 x 10-5 and c = 1.1 i = 5% Y is the present value random variable for this annuity. Calculate the probability that Y is less than $11,500. QUESTION 3 You are given: Hx+c = 0.05, fort 20 8 = 6% Y is the present value random variable for a continuous whole life annuity of $1 issued to (x). Calculate Pr[Y 2 E(Y) - Var(Y)]