11. [Total: 40 marks] For a contract of 25-year endowment insurance of 100,000 on (40), the following pricing assumptions are given: Death benefit is payable at the end of the year of death. Premium is payable at the beginning of each year until the death or endowment benefit is paid. Mortality follows the Standard Ultimate Life Table. i=0.05. . (a) [5 marks] Calculate the net level premium P for this contract. (b) [5 marks] Write down the net future loss random variable L" as a function of the curtate future lifetime random variable K and using the net level premium P in part (a). (c) [5 marks] Evaluate the net future loss random variable at K= 23 and 24. (d) [5 marks] Calculate P(01">0). (e) The following expense assumptions are given: 90% of the first premium, 15% of the second to tenth premiums and 0% of all premiums thereafter, payable at the time of premium payment. 300 at the beginning of the first year and 100 at the beginning of each year thereafter. 500 settlement expense. (i) [5 marks) Write down the gross future loss random variable oL' as a function of the curtate future lifetime random variable K and with a gross level premium G. (ii) [5 marks] Suppose that the gross level premium G is 120% of the net level premium P, calculate E(,1%). (iii) [5 marks] What is the gross level premium G based on the equivalence principle? (iv) 15 marks] Explain the concept of new business strain using the gross level premium G obtained in part (iii) as an illustration. 11. [Total: 40 marks] For a contract of 25-year endowment insurance of 100,000 on (40), the following pricing assumptions are given: Death benefit is payable at the end of the year of death. Premium is payable at the beginning of each year until the death or endowment benefit is paid. Mortality follows the Standard Ultimate Life Table. i=0.05. . (a) [5 marks] Calculate the net level premium P for this contract. (b) [5 marks] Write down the net future loss random variable L" as a function of the curtate future lifetime random variable K and using the net level premium P in part (a). (c) [5 marks] Evaluate the net future loss random variable at K= 23 and 24. (d) [5 marks] Calculate P(01">0). (e) The following expense assumptions are given: 90% of the first premium, 15% of the second to tenth premiums and 0% of all premiums thereafter, payable at the time of premium payment. 300 at the beginning of the first year and 100 at the beginning of each year thereafter. 500 settlement expense. (i) [5 marks) Write down the gross future loss random variable oL' as a function of the curtate future lifetime random variable K and with a gross level premium G. (ii) [5 marks] Suppose that the gross level premium G is 120% of the net level premium P, calculate E(,1%). (iii) [5 marks] What is the gross level premium G based on the equivalence principle? (iv) 15 marks] Explain the concept of new business strain using the gross level premium G obtained in part (iii) as an illustration