Q1 need all parts

A disability income insurance model has three states: State 0 (Healthy), State 1 (Sick), and State 2 (Dead). All transitions occur at the end of the year. You are given i=0.06 and the transition matrix P[t0]=0.70.400.20.400.10.21. For a 3-year term assurance issued to a healthy policyholder aged x, you are given: - This assurance pays a death benefit of 5000 at the end of the year of death. - This assurance pays 1000 as long as the policyholder is sick at the start of each year. - This assurance pays an endowment benefit which is a refund of the net single premium without interest. - P is the net single premium for this assurance policy. - tV is the net premium reserve at time t for this assurance policy. (a) Calculate 2px00,2px01 and 2px02. [3 marks] (b) Calculate the expected present value of: i. The death benefit ii. The sick benefit iii. The endowment benefit (as a function of P ) [12 marks ] (c) Calculate P. [2 marks] (d) Calculate 2V(i) for i=0,1,2 and hence the expected value of 2V. A disability income insurance model has three states: State 0 (Healthy), State 1 (Sick), and State 2 (Dead). All transitions occur at the end of the year. You are given i=0.06 and the transition matrix P[t0]=0.70.400.20.400.10.21. For a 3-year term assurance issued to a healthy policyholder aged x, you are given: - This assurance pays a death benefit of 5000 at the end of the year of death. - This assurance pays 1000 as long as the policyholder is sick at the start of each year. - This assurance pays an endowment benefit which is a refund of the net single premium without interest. - P is the net single premium for this assurance policy. - tV is the net premium reserve at time t for this assurance policy. (a) Calculate 2px00,2px01 and 2px02. [3 marks] (b) Calculate the expected present value of: i. The death benefit ii. The sick benefit iii. The endowment benefit (as a function of P ) [12 marks ] (c) Calculate P. [2 marks] (d) Calculate 2V(i) for i=0,1,2 and hence the expected value of 2V