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The AM92 table is based on the mortality of assured male lives in the UK. (i) As there is no corresponding mortality table for female lives, in order to calculate survival probabilities for female policyholders, an actuary decides to use the AM92 table, but with an 'age rating' of 4 years applied, ie a female aged x is considered to experience mortality equivalent to a male aged x-4. (a) Explain the rationale underlying this approach. (b) Calculate the probability that a female policyholder aged 62 survives for at least the next 10 years. (ii) A male policyholder aged 65 is known to be in poor health, and it has been determined that his mortality is 200% of AM92 Ultimate, ie he is subject to q, values equal to twice those of the AM92 Ultimate table. Calculate the probability that this policyholder will die before age 67. A select life table is to be constructed with a select period of two years added to the ELT15 (Males) table, which is to be treated as the ultimate table. Select rates are to be derived by applying the same ratios select : ultimate seen in the AM92 table, ie: qixl q, and q1x]+1 =- 9[ * 1+1 qx+1 9 x +1 where the dash notation q, refers to AM92 mortality. Calculate the value of /160] . The table below is part of a mortality table used by a life insurance company to calculate probabilities for a special type of life insurance policy. X 1 x/+1 1 x/+2 4x1+3 /x+4 51 1,537 1,517 1,502 1,492 1,483 52 1,532 1,512 1,497 1,487 1,477 53 1,525 1,505 1,490 1,480 1,470 54 1,517 1,499 1,484 1,474 1,462 55 1,512 1,492 1,477 1,467 1,453 (i) Calculate the probability that a policyholder who was accepted for insurance exactly 2 years ago and is now aged exactly 55 will die between age 56 and age 57. (ii) Calculate the corresponding probability for an individual of the same age who has been a policyholder for many years. (mii) Comment on your answers to (i) and (ii)..8 Given that Pgp =0.988 , calculate o.s/go assuming: (i) a uniform distribution of deaths between integer ages a constant force of mortality between integer ages. 9 Calculate the value of 1 75PASs using AM92 Ultimate mortality and assuming that: tyle (1) deaths are uniformly distributed between integer ages. [3] (i) the force of mortality is constant between integer ages. [3] [Total 6]