An insurance company issues a whole life insurance to (20). The death benefit of $1,000,000 is payable at the end of month of death. The policy is purchased with monthly premium P. An expense of $100 is incurred at the time of issue of the policy. An expense of 0.03P is incurred at each premium payment including the first one. You are given that a(12) = 1.00020 and B(12) = 0.46651. Assume UDD and Standard Ultimate Survival Model. Assume i = 5%.
(a) Calculate the monthly premium P using the equivalence principle.
(b) Calculate the policy value at the end of the first month, i.e., 12