Part B. Solve the following problems. You must show your work! (70 points). #1. (20 pts) William is 40 years old and purchases a 25 year term life insurance policy with face value of $150000 payable at the end of the year of death. This policy will be paid by a level benefit annual premium of $3423 at the beginning of the next 25 years while William is alive. Assume that i = 6.5% and death is modeled using de Moivre's model with terminal age 90. Calculate the probability that the loss is positive. #2. (25 pts) For a special fully discrete 3-year term insurance on (x): k 4.5+k for k=0 0 0.200 (i) bk+1 (iii) i = 0.06 1,000(11 - k) for k = 1,2 1 0.100 20.097 Calculate the level annual benefit premium for this insurance. = -4.00 (ii) #3. (25 pts) For a special fully discrete 35-payment whole life insurance on (30): (i) The death benefit is 1 for the first 20 years and is 5 thereafter. (i) The initial benefit premium paid during the each of the first 20 years is one fifth of the benefit premium paid during each of the 15 subsequent years. (iii) Mortality follows the Illustrative Life Table. (iv) i = 0.06 (v) A30:20 = 0.32307. (vi) 30:33 = 14.835 Calculate the initial annual benefit premium