10. Joe, age 50, has a constant force of mortality of 0.8% for the next 20 years. After that, death is uniformly distributed from age 70 to age 110. The force of interest is 4%. a) What is the net loss function for an insurance policy being paid for by a continuous annuity of $1665 per year for life, and which pays $100,000 at the moment of death? (you do not need the survival function for this) b) What is the break-even time and age of death? c) What is the survival function for Joe? (make sure it is continuous at t=20) d) What is the probability that the insurance company will take a loss on this policy? Optional bonus marks: e) Confirm that $1664.47 per year is the appropriate net premium. 10. Joe, age 50, has a constant force of mortality of 0.8% for the next 20 years. After that, death is uniformly distributed from age 70 to age 110. The force of interest is 4%. a) What is the net loss function for an insurance policy being paid for by a continuous annuity of $1665 per year for life, and which pays $100,000 at the moment of death? (you do not need the survival function for this) b) What is the break-even time and age of death? c) What is the survival function for Joe? (make sure it is continuous at t=20) d) What is the probability that the insurance company will take a loss on this policy? Optional bonus marks: e) Confirm that $1664.47 per year is the appropriate net premium