Question 2a)

MATLAB: All computing tasks must be done using MATLAB.

Show Your Work: Please show your work, not just the answers.

2. Mortality, Endowment, and Life Annuities (20 marks) (a) The 2019 graduating class of a boy's college contained 100 males aged 18 and 50 aged 19. How many can be expected to survive for the class reunion in 2029? (5 marks) (b) Mrs Angel wants to help her 18 years old grandson Bill buy a house a few years after he graduates from the University. She therefore pays $40,000 for a pure endowment which will pay a benefit to Bill on his survival to age 24. Assume the effective interest rate is 2% p.a. (10 marks): (i) How much will this survival benefit be? (5 marks) 2 (ii) Find the difference of the endowment amount compared to the accumulated value of the money in a savings account at r = 2%. (5 marks) (c) On his 20th birthday, Curry inherits $50,000 from his uncle, and he uses it to buy a 5-year temporary life annuity. Assume that = 4%. Find the annual payment that is made at the end of each year starting at age 65 for 5 years. (5 marks) r(1) 2. Mortality, Endowment, and Life Annuities (20 marks) (a) The 2019 graduating class of a boy's college contained 100 males aged 18 and 50 aged 19. How many can be expected to survive for the class reunion in 2029? (5 marks) (b) Mrs Angel wants to help her 18 years old grandson Bill buy a house a few years after he graduates from the University. She therefore pays $40,000 for a pure endowment which will pay a benefit to Bill on his survival to age 24. Assume the effective interest rate is 2% p.a. (10 marks): (i) How much will this survival benefit be? (5 marks) 2 (ii) Find the difference of the endowment amount compared to the accumulated value of the money in a savings account at r = 2%. (5 marks) (c) On his 20th birthday, Curry inherits $50,000 from his uncle, and he uses it to buy a 5-year temporary life annuity. Assume that = 4%. Find the annual payment that is made at the end of each year starting at age 65 for 5 years. (5 marks) r(1)