A 2-year term insurance contract sold to two lives, (70) and (71), provides for benefits payable at the end of the year of the first death. The benefit paid is 40 in the first year and 50 in the second year. You are given that q70 = 0.4, q71 = 0.5, q72 = 0.6, and the interest rate is 100%. Let Z denotes the present value of the benefits.
(a) Find E(Z) and Var(Z).
(b) Suppose the contract is to be paid for by level annual premiums of P payable for 2 years. What should P be if the equivalence principle is used, and what is the resulting probability that L ≤ 0?
(c) What is the smallest amount that P could be if we want a probability of at least 0.25 that the loss L will be less than or equal to 0?