For a special fully discrete whole life insurance on (x), you are given: The death...

 

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For a special fully discrete whole life insurance on (x), you are given: • The death benefit, db, is payable at the end of the year of death: i. ii. iii. dbt • The benefit premiums are: a b c ,t = 1,...,20 t = 21,21,...,30 ,t = 31,32... avqx+t t= 0,1,...,19 IL ,t = 20,21,...,29 cvqx+t t = 30,31, ... Determine 7 in terms of the standard actuarial notation so that the E[L] = 0. Draw the timeline and express the benefit reserve, V at the point k = 10, k = 20 and k = 30 in algebraic terms. Express the tenth-year terminal prospective loss in algebraic terms if the policyholder dies in the 27th year. (15 marks) For a special fully discrete whole life insurance on (x), you are given: • The death benefit, db, is payable at the end of the year of death: i. ii. iii. dbt • The benefit premiums are: a b c ,t = 1,...,20 t = 21,21,...,30 ,t = 31,32... avqx+t t= 0,1,...,19 IL ,t = 20,21,...,29 cvqx+t t = 30,31, ... Determine 7 in terms of the standard actuarial notation so that the E[L] = 0. Draw the timeline and express the benefit reserve, V at the point k = 10, k = 20 and k = 30 in algebraic terms. Express the tenth-year terminal prospective loss in algebraic terms if the policyholder dies in the 27th year. (15 marks)