A 3-year life annuity on (x) and (y) provides for annuity benefits of 1 at time 0, 2 at time 1 and 4 at time 2, provided that both individuals are alive. You are given that px = 0.8, 2px = 0.6, py = 0.7, 2py = 0.5 and the interest rate is a constant 100%.
(a) Find the expectation and variance of the present value of the benefits.
(b) A single premium for the contract is found by adding a 20% relative risk loading to the present value. What is the probability that the premium will be sufficient to provide for the benefit payments on a single contract?