(2) (10 pts) Consider a whole life insurance with annual, beginning-of-year premiums, in the amount of P, issued to a select life aged 40, with sum insured 200,000, payable at the end of year of death. The premiums are to be paid for a maximum of 30 years. (a) (3 points) Write down an expression for the net future loss random variable. (b) (4 points) Calculate the net annual premium Pusing the equivalence principle, assuming SSSM and an annual effective interest rate of i = 5%. (c) (3 points) Calculate the probability that the insurance company makes a profit from this contract. (2) (10 pts) Consider a whole life insurance with annual, beginning-of-year premiums, in the amount of P, issued to a select life aged 40, with sum insured 200,000, payable at the end of year of death. The premiums are to be paid for a maximum of 30 years. (a) (3 points) Write down an expression for the net future loss random variable. (b) (4 points) Calculate the net annual premium Pusing the equivalence principle, assuming SSSM and an annual effective interest rate of i = 5%. (c) (3 points) Calculate the probability that the insurance company makes a profit from this contract