(Question taken from a previous SOA exam)undefinedA whole life annuity issued to a life age 40 pays $2,000 a year at the beginning of each year for the first 10 years and then $3,000 a year thereafter. undefinedUsing the SOA’s Standard Ultimate Life Table at i = .05 (which was distributed in class), calculate the expected present value of this annuity.2. Johnage 55 has terminated employment from the XYZ company. He has earned a life pensionbenefit of $1,000 per month (paid beginning of month) starting at age 65.Johnis given the choice of starting his benefit earlier than age 65 at a reducedamount that is actuarially equivalent to the age 65 benefit.Usingthe SOA’s Standard Ultimate Life Table at i = .05 (which was distributed inclass) and Woolhouse’s 2 term approximation for 1/mthly, calculate the monthlyreduced lifetime benefit starting at age 55.A ten-year term insurance is be issued to a life aged 50. The sum insured is $200,000 and payable immediately upon death. Premium payments are annual in advance.a) Using the SOA Standard Ultimate Life Table at i = 5% and UDD, compute the net annual premium determined by the equivalence principle. b) Find the probability that this contract makes a profit. c) Compute the gross premium determined by the equivalence principle if the initial expense is $500 plus 10% of the first premium, and if there is a renewal expense of 2% of the annual premium payment for the second and all subsequent premium payments.
