. . Premiums/Reserves Question 1 (5 marks) You work for an insurance company that sells 30-year term life insurance policies. The actuarial assumptions used by the insurance company are: Mortality is exponentially distributed, with constant u = 0.03 The actual interest rate is assumed to be 7% pa annual effective The rate of interest used for pricing is 6% pa annual effective Benefits are paid at the time of death 0) Using the equivalence principle, what single premium would someone aged exactly 35 years pay for a benefit of $100,000 paid at the time of death? i) What is the expected profit on the policy at issue? ii) If the premium is invested until the benefit is paid, what is the profit or loss at the time of death if the policyholder dies aged exactly 45? iv) If the premium is invested until the benefit is paid, what is the profit or loss at the time of issue if the policyholder dies aged exactly 61? . . . Premiums/Reserves Question 1 (5 marks) You work for an insurance company that sells 30-year term life insurance policies. The actuarial assumptions used by the insurance company are: Mortality is exponentially distributed, with constant u = 0.03 The actual interest rate is assumed to be 7% pa annual effective The rate of interest used for pricing is 6% pa annual effective Benefits are paid at the time of death 0) Using the equivalence principle, what single premium would someone aged exactly 35 years pay for a benefit of $100,000 paid at the time of death? i) What is the expected profit on the policy at issue? ii) If the premium is invested until the benefit is paid, what is the profit or loss at the time of death if the policyholder dies aged exactly 45? iv) If the premium is invested until the benefit is paid, what is the profit or loss at the time of issue if the policyholder dies aged exactly 61