Kindly please show workings on paper.

Question 5 [15 marks] Today is 1 January 2018. Alec is 85 years old. Alec is considering paying a single premium to purchase a life annuity product with a death benefit cover. This product pays $20,000 at the end of each year Alec is alive. This product also pays $5,000 at the end of the year of death. The probabilities of Alec surviving over the next 4 years are stated in table 4. Year Table 4: Survival probabilities Probability of surviving from start of year to end of year 0.9 0.67 0.38 0 2 3 4 The insurance company incurs initial expenses of $100 per policy at the be ginning of the term of the insurance. The interest rate is ji = 3.5% p.a. a. [5 marks] Carefully draw a contingent cash flow diagram that models this annuity policy from the perspective of the insurance company. b. [2 marks] Calculate Alec's probabilities of being alive on 1 January 2019, 1 January 2020, 1 January 2021 and 1 January 2022. Round your answer to five decimal places c. (4 marks] Calculate Alec's probabilities of dying in each of years 2018, 2019, 2020 and 2021. Round your answer to five decimal places. d. [4 marks] Calculate the value of Alec's fair single premium which is paid on the issue date of this policy. Round your answer to two decimal places. 7