An actuary prices a special 3-year policy based on the following homogenous Markov Chain transition probability matrix. State 1 is healthy, State 2 is disabled, state 3 is withdrawn and state 4 is dead. 0.6 0.2 0.15 0.05 0.2 0 P = 0.3 0.5 0 0 0 1 0 0 0 1 You are given: (i) Transitions occur instantaneously at the end of each year (ii) Death benefit is 100,000 payable at the end of the year of death. (iii) The disability is 25,000 payable at the start of each year when insured is disabled at that time. (iv) Annual effective interest rate is 0.06. Consider a healthy insured at time 0, calculate: (a) (1 points) the probability that the insured will be in healthy state after the policy terminates (b) (4 points) the net annual premium. Premium is waived when insured is in disability. (c) (4 points) Let V and V(2) be net premium reserve at time t when the insured is in state 1 and 2, respectiv Calculate (1) 2V(1) (11) 2V (2) An actuary prices a special 3-year policy based on the following homogenous Markov Chain transition probability matrix. State 1 is healthy, State 2 is disabled, state 3 is withdrawn and state 4 is dead. 0.6 0.2 0.15 0.05 0.2 0 P = 0.3 0.5 0 0 0 1 0 0 0 1 You are given: (i) Transitions occur instantaneously at the end of each year (ii) Death benefit is 100,000 payable at the end of the year of death. (iii) The disability is 25,000 payable at the start of each year when insured is disabled at that time. (iv) Annual effective interest rate is 0.06. Consider a healthy insured at time 0, calculate: (a) (1 points) the probability that the insured will be in healthy state after the policy terminates (b) (4 points) the net annual premium. Premium is waived when insured is in disability. (c) (4 points) Let V and V(2) be net premium reserve at time t when the insured is in state 1 and 2, respectiv Calculate (1) 2V(1) (11) 2V (2) An actuary prices a special 3-year policy based on the following homogenous Markov Chain transition probability matrix. State 1 is healthy, State 2 is disabled, state 3 is withdrawn and state 4 is dead. 0.6 0.2 0.15 0.05 0.2 0 P = 0.3 0.5 0 0 0 1 0 0 0 1 You are given: (i) Transitions occur instantaneously at the end of each year (ii) Death benefit is 100,000 payable at the end of the year of death. (iii) The disability is 25,000 payable at the start of each year when insured is disabled at that time. (iv) Annual effective interest rate is 0.06. Consider a healthy insured at time 0, calculate: (a) (1 points) the probability that the insured will be in healthy state after the policy terminates (b) (4 points) the net annual premium. Premium is waived when insured is in disability. (c) (4 points) Let V and V(2) be net premium reserve at time t when the insured is in state 1 and 2, respectiv Calculate (1) 2V(1) (11) 2V (2)