A 2-year term insurance policy on (50), with a constant death benefit of 1000, is purchased by two-level annual premiums. Policyholders who choose to lapse the policy at time 1 will receive 1V as a cash value. Assume that mortality and interest follow the projected pattern, and that the premium charged is the net premium. Suppose, however, that a typical group of people age 51 who have purchased insurance at age 50 can be divided into two groups. Half of them are healthy and half are not. The non-healthy group can expect to have twice as many deaths over the following year as the healthy group. Suppose that q51 = 0.03. What is the loss on each remaining policy for the second year, assuming:
(a) All of the healthy policyholders at age 51 lapse the policy at that time, and none of the unhealthy ones do;
(b) One-half of the healthy policyholders, and one-quarter of the unhealthy policy- holders, lapse the policy at age 51.