2. [15 points) Cathy is 85 years old. She considers to buy an annuity that pays $20,000 at the end of each policy year if she is alive till her death or 90 years old, whichever is earlier. Sunlife offers a single premium annuity product (i.e. only one premium payment at the start) based on the following mortality table. Assume that interest rates are 3% per annum for all maturities (with continuous compounding). What is the fair premium Sunlife should charge? Age 85 86 87 88 89 Prob of death in 1 year 0.07 0.075 0.085 0.1 0.12 Table 1: Mortality table for females 2. [15 points) Cathy is 85 years old. She considers to buy an annuity that pays $20,000 at the end of each policy year if she is alive till her death or 90 years old, whichever is earlier. Sunlife offers a single premium annuity product (i.e. only one premium payment at the start) based on the following mortality table. Assume that interest rates are 3% per annum for all maturities (with continuous compounding). What is the fair premium Sunlife should charge? Age 85 86 87 88 89 Prob of death in 1 year 0.07 0.075 0.085 0.1 0.12 Table 1: Mortality table for females