I am struggling to understand the solution to q1.8 in the Q&A bank for CT5. The first line of the solution gives E[g(k)] = (D50 / D40) * a50:25 where the annuity is paid in advance. I know the ratio (D50 / D40) is the discount factor, but can anyone explain where the annuity comes from? I am confused as the life is aged 40 now, not 50. Should it not be an annuity at age 40, deferred for 10 years. Page 16 of Chapter 2 says "similarly expressions can be derived for n year annuties deferred for m years". Is the solution to this question applying these? Can anyone explain how these formulae are derived. Thanks in advance for any help.
Hi Cathy, So this is a 25 yr annuity, deferred for 10 years from age 40. I think the symbol for that is 10|a40:25. Either way, by conditioning on survival to 50 it is P(still alive at 50) * E(v^10* value of annuity at age 50|life still alive at age 50) = v^10* 10p40 * a50:25 You can use the same argument to derive the general formula. Any help? Louisa
