In this problem all death benefits are payable at the moment of death, and all premiums are payable continuously at a level rate. A life insurance contract on (x) and (y) provides for death benefits as follows. If (x) dies first at time t, the amount paid is the reserve at time t on a 1-unit whole life insurance on (y) with premiums payable for life. If (y) dies first at time t, the amount paid is the reserve at time t for a 1-unit whole life insurance on (x) with premiums payable for life. Premiums are payable until the first death. Show that the rate of premium payment is P_x + P_y - P_xy, where P_x denotes the rate of premium payment for a 1-unit whole life insurance on x with premiums payable for life, and P_y and P_xy denote similar quantities for y and xy, respectively. You should demonstrate this mathematically and also give a verbal explanation.