Answer macroeconomics questions

A life aged 40 effects a 25-year without profits endowment assurance policy with a sum assured of $50,000 (payable at the end of the year of death or on survival to the end of the term). Level premiums are payable annually in advance throughout the term of the policy or until earlier death of the life assured. Calculate the level premium, P, using the following premium basis Mortality: A1967-70 Ultimate; Interest: 6% p.a. Expenses: none An office issues a large number of 25-year without-profit endowment assurances on lives aged exactly 40. Level annual premiums are payable throughout the term, and the sum assured of each policy is f10,000, payable at the end of the year of death or on survival to end of the term. The office's premium basis is: A1967-1970 ultimate; 4% p.a. interest; expenses are 5% of each annual premium including the first, with additional initial ex- penses of 1% of the sum assured. Calculate the annual premium for each policy. .3 A 5-year temporary assurance, issued to a woman aged 55, has a sum assured of $50,000 in the first year, reducing by f10,000 each year. The sum assured is payable at the end of the year of death. Level premiums, limited to at most 3 years' payments, are payable annually in advance. Calculate the annual premium. Basis: A1967-1970 select mortality 1% p.a. interest expenses are 10% of all office premiums(i) Show that the CRLB for unbiased estimators of / , based on a random sample of n observations from a N(u,o') distribution with known variance o', is given by n Hint: Use the results from Example 10.4. ii) Show that the variance of the maximum likelihood estimator / = X attains the CRLB