question: If the policyholder dies during the term, an income benefit of £5,000 pa is payable for the remainder of the five years, the first payment being made on the policy anniversary following death, and the final payment being made at the end of the fifth policy year. answer : the solution as per the question bank , PV death payments=5,000(0.01v+0.0219v2+.....+ 0.0573v5) but i feel it should have been , =5000(0.01v+0.0219v2+......+ 0.0573v5) ,if death occurs in the first yr the benefit is paid for remaining 5 years + 5000(0.0219v2+......+ 0.0573v5) , if death occurs in the 2nd yr , the benefit is paid for remaining 3 yrs, and so on . it should be in terms of an annuity factor and not just discount factor . kindly enlighten .
Under your suggested method, you would be double counting. The probabilities given are the probability of being in a particular state at the end of a particular year, ie the sum of the H, S, D probabilities sum to 1 for each year. If you look at the table of probabilities in part (i), you'll see that the probability of being dead at the end of year 2 is calculated as: the probability of being healthy at the end of year 1 and then dying during year 2 plus the probability of being sick at the end of year 1 and then dying during year 2 plus the probability of being dead at the end of year 1 (and hence still being dead at the end of year 2). Under your method, you'd be adding in this last term again. I haven't gone through it in detail, but I suspect that your method would work if you use a different set of probabilities.
