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Exercises 4.1 The following is an extract from a life table with a select period of 1 year. Age r age r + 1 55 90. 636 00.032 56 56 89. 739 89, 132 57 88, 151 58 87,004 59 85,874 60 84.586 61 Evaluate assa and a paja at 5 % per annum interest. 4.2 Given that a, = 20, dam = 18 and dren =8, find the values of , E, and arm. 4.3 (i) Write down an expression for a, in terms of v, Pr, and arti. (ii) On a certain select mortality table the select period is one year. Express ajj in terms of ", Ply] and arti. Given that qp] = .6q, and that at 41% $1 p.a. interest ass = 15.719 and as = 15.509, find the value of apj (at the same rate of interest). 4.4 Using the A1967-70 table with 4% p.a. interest find the values of "(ojao. 419+1:0 94030, (Ja)o, sapojim, s(la):2 4.5 (i) Find the present value of a deferred annuity of f1000 pa. to a man aged 40. Payments commence on his 60th birthday, if he is then alive, and continue thereafter annually for life Basis: A1967-70 ultimate mortality, 4 % p.a. interest. (ii] As above, but select mortality (at entry.) (iii) As above, but A1967-70 ultimate mortality to exact age 60 and a(55) males ultimate mortality above exact age 60. 4.6 According to a certain mortality table, which has a select period of 1 year and is such that 4/x] = 0.6q, for each I, ago at 10% interest = 5.641, and, dzi at 10% interest = 5.449. Find apoj at 10% interest.Example 5.8.1. Ten years ago a woman aged exactly 35 effected an assurance policy by level annual premiums payable for a maximum of 25 years. The policy provided the following benefits: (i) a whole life assurance benefit of 42, 000 payable at the end of the year of death, (ii) a family income benefit of term 25 years, with payments of 6300 per month, beginning im- mediately on death, if this occurs within 25 years. The final payment is made in the month ending 25 years after the issue date. Calculate the annual premium on the basis given below: A 1967-70 0% interest expenses are 3% of all premiums