Long Term Actuarial Math class

(2) A fully discrete 30-year term insurance on (40) is available in two options: Option l: Death benefit of 1,000 is payable at the end of the year of death Option II: Death benefit of 1,000 plus the net premium reserves is payable at the end of the year of death The net annual level premium for Option I is 14.29560, and net annual level premium for Option Il is 16.61658. Let k V be the time-k net premium reserve for Option I, and V' is the time-k net premium reserve for Option II. (a) If 1 V 11.95120, and 1 V 14.32975; determine the level interest rate used in calculating the reserves. (5 points) (b) Calculate the difference of 29 V and 29 V' using the interest rate from (a) (5 points) (c) If 12 V 146.5143, 12 V' 175.1465, and 11 V 134.9784, using the interest rate from (a) calculate 11 V' (6 points) (2) A fully discrete 30-year term insurance on (40) is available in two options: Option l: Death benefit of 1,000 is payable at the end of the year of death Option II: Death benefit of 1,000 plus the net premium reserves is payable at the end of the year of death The net annual level premium for Option I is 14.29560, and net annual level premium for Option Il is 16.61658. Let k V be the time-k net premium reserve for Option I, and V' is the time-k net premium reserve for Option II. (a) If 1 V 11.95120, and 1 V 14.32975; determine the level interest rate used in calculating the reserves. (5 points) (b) Calculate the difference of 29 V and 29 V' using the interest rate from (a) (5 points) (c) If 12 V 146.5143, 12 V' 175.1465, and 11 V 134.9784, using the interest rate from (a) calculate 11 V' (6 points)