A common shock model for a couple, Husband aged x and Wife aged y, has four states: State o (Both are alive), State 1 (Wife is dead), State 2 (Husband is dead), and State 3 (Both are dead). For t > 0, you are given: 01 . Mx+t:y+z = 0.02 . - 0.02 02 kitty+t 03 13 Mx+ty+t = 0.01 urtt = 0.07 Mtt = 0.07 23 t = 0.03 Both Husband and Wife purchase a fully continuous 20-year term insurance that pays 1000 at the moment of the first death. Premiums are payable for 10 years. No benefit will be paid if both Husband and Wife die at the same time. The net premium reserve at time 19.5 given that both Husband and Wife are still alive at that time is 19.5V(0) (a) Calculate the net annual premium. (b) Calculate the exact value of 19.5V(0) (6) Approximate 19.5V) using Euler's backward method with h = 0.25. A common shock model for a couple, Husband aged x and Wife aged y, has four states: State o (Both are alive), State 1 (Wife is dead), State 2 (Husband is dead), and State 3 (Both are dead). For t > 0, you are given: 01 . Mx+t:y+z = 0.02 . - 0.02 02 kitty+t 03 13 Mx+ty+t = 0.01 urtt = 0.07 Mtt = 0.07 23 t = 0.03 Both Husband and Wife purchase a fully continuous 20-year term insurance that pays 1000 at the moment of the first death. Premiums are payable for 10 years. No benefit will be paid if both Husband and Wife die at the same time. The net premium reserve at time 19.5 given that both Husband and Wife are still alive at that time is 19.5V(0) (a) Calculate the net annual premium. (b) Calculate the exact value of 19.5V(0) (6) Approximate 19.5V) using Euler's backward method with h = 0.25