Please solve using actuarial notation. I will upvote is the solution is correct. Thank you so much!

15. A fully discrete 3-year endowment insurance with annual premiums and face amount $100,000 is issued to (2). Interest on the policy is at annual effective rate 10% and mortality rates are qu = .1, 9x+1 = 2 and q3+2 = .3. You are given that the net annual premium is $32,347. (a) (2 point) Calculate the 3rd year initial reserve via both the prospective and retrospective method. (b) (2 points) Suppose that the policy holder survives to the end of the 3-year policy period. Calculate the net-loss-at-issue. Explain briefly under what circumstances a policy can have a negative loss-at-issue. (c) (4 points) Formulate L the net-loss-at-issue as a random variable in point-by-point form and verify that E[L] = 0. Calculate P[L > 0). 15. A fully discrete 3-year endowment insurance with annual premiums and face amount $100,000 is issued to (2). Interest on the policy is at annual effective rate 10% and mortality rates are qu = .1, 9x+1 = 2 and q3+2 = .3. You are given that the net annual premium is $32,347. (a) (2 point) Calculate the 3rd year initial reserve via both the prospective and retrospective method. (b) (2 points) Suppose that the policy holder survives to the end of the 3-year policy period. Calculate the net-loss-at-issue. Explain briefly under what circumstances a policy can have a negative loss-at-issue. (c) (4 points) Formulate L the net-loss-at-issue as a random variable in point-by-point form and verify that E[L] = 0. Calculate P[L > 0)