Hi, In this question the member can only retire at age 65. Does this not make the use of the pensions table invalid? The solution has r_65/I_45 as the probability that they'll retire at 65, but the r_65 (and I_65) being equal to 3757 assumes that there are retirement decrements between 60 and 65. So the probability r_65/I_45 used in the solution is effectively allowing for the probability of retiring at other ages. Am I misunderstanding something here?
No, you are understanding this very well indeed In fact, you have gone the extra step and really understood the implication of what "only retiring at 65" means. So, if this happened in practice, and all you had was the service table given in the orange book, then you would have to construct a revised service table in which forces of normal retirement were all set equal to zero until age 65 (at which point 100% of all still-active members would retire). This would effectively increase the probability of the 45-year old ending up as a normal retirement at age 65 (actually quite considerably). In the exam? For 4 marks they cannot conceivably be wanting you to do this! Also, you can be absolutely certain that if they had intended a revised table to be constructed they would have spelt this out quite clearly, would only have involved a year or two (not 20) and given quite a few more marks for it. How should you deal with this in the exam - ie where you think the question is wrong? One approach is to describe what you think you should do had you enough time to do it. Then explain that instead you would just use the service table as provided, and make the point that by doing so we are therefore assuming people continue to retire at earlier retirement ages but don't get any pension benefit (ever!) if they do so. And if you politely point out that you believe this to be wrong, then you can't be criticised for doing this. However, probably the best approach (in this case) would be to explain exactly what you think is needed to answer the question correctly and why, describing the steps you would carry out. Include the formulae you would use for calculating the values in this, or you might miss some of the marks. Then say that there is insufficient time available to do this in the exam, so you have not attempted it. (I think your explanation would be worth 4 marks.) So, full marks from me for spotting this. Good luck Robert
