Question 1: A male aged 50 purchases an endowment with a term of 20 years and a sum assured of S 10,000. Use as a basis the AM92 Ultimate mortality tables, an effective rate of interest of 5% p.a. and assume initial expenses of $100 and ongoing expenses of $20 subject to 1.5% inflation p.a- Find the premium that should be paid, assuming: a) Premiums are paid annually in advance and benefits are paid at the end of the policy year. [l mark] b) Premiums are paid annually in advance and benefits are paid immediately upon death. [l mark] c) Premiums are paid monthly in advance and benefits are paid immediately upon death [l mark] Question 2: The followin is an extract from a life table with a select riod ofl ear. Age x 55 56 90 636 89 739 90 032 89 132 88 151 87 094 85 974 84 586 Age x + 1 56 57 58 59 60 61 [2 marks] Evaluate and at 5% interest per annum_ 56:Sl [561:Sl Question 3: An annuity is to be paid annually in arrears to a life aged 40 for a maximum of 15 years, but ceases on death. It is to be purchased by a single premium of $10,000 using as basis the AM92 select mortality table and 4% interest p.a. a) Find the amount of the annual annuity payments. [l mark] b) If the present value ofthe actual number of premiums paid is less than Sl 0,000, the company selling the annuity will make a profit. Find the probability that this will happen. [l mark] c) Now suppose the payments are not to start until the life is aged 55, as long as the policyholder is still alive at that stage. Recalculate the annuity payment under this scenario. [l mark] Question 4: Assume that deaths within a given year of age, x, are uniformly distributed across the year. In other words, for O t 1, we have IX+t = lx tdx. Under this assumption, find an expression for t_sqx+s in terms of O s t 1 and qx = dx/lx. [2 marks]