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S&AS: STAT3901 Life Contingencies 10. The force of mortality of an impaired life aged at is given by HI) = 140+ 00% 7 where Mac) is the standard force of mortality for a normal life aged 13. (a) (b) Assume that My) is constant for all It For a normal life, (111)I and (iii): calculated at a constant force of interest are 100 and 47 respectively Find (f (1,); and (ill); for an impaired life. [5 marks] A life ofce issues a $l00,000 endowment insurance with an 71-year term to an impaired life aged at. The death benet is payable at the end of the year of death. Level premiums are to be paid at the start of each year if the life is alive. The initial expenses are 30% of the rst premium and the renewal expenses are 5% of each premium except the rst. The claim expenses are $100. Assuming that the force of interest 6 = 0.0257 express the level annual premium in terms of 251m, that is, the actuarial present value of an nyear temporary life annuity-due for a normal life evaluated at 26. [5 marks] [Total: 10 marks]