The following attachment questions seeks your assistance

Example 7.1 Consider a 20-year endowment policy purchased by a life aged 50. Level premiums are payable annually throughout the term of the policy and the sum insured, $500 000, is payable at the end of the year of death or at the end of the term, whichever is sooner. The basis used by the insurance company for all calculations is the Standard Select Survival Model, 5% per year interest and no allowance for expenses. (a) Show that the annual net premium, P, calculated using the equivalence principle, is $15 114.33. (b) Calculate E[L"'] fort = 10 andt = 11, in both cases just before the premium due at time t is paid.Example 7.2 An insurer issues a whole life insurance policy to a life aged 50. The sum insured of $100 000 is payable at the end of the year of death. Level premiums of $1300 are payable annually in advance throughout the term of the contract. (a) Calculate the gross premium policy value five years after the inception of the contract, assuming that the policy is still in force, using the following basis: Survival model: Standard Select Survival Model Interest: 5% per year effective Expenses: 12.5% of each premium (b) Calculate the net premium policy value five years after the issue of the contract, assuming that the policy is still in force, using the following basis: Survival model: Standard Select Survival Model Interest: 4% per yearExample 7.3 A woman aged 60 purchases a 20-year endowment insurance with a sum insured of $100 000 payable at the end of the year of death or on survival to age 80, whichever occurs first. An annual premium of $5200 is payable for at most 10 years. The insurer uses the following basis for the calculation of policy values: Survival model: Standard Select Survival Model Interest: 5% per year effective Expenses: 10% of the first premium, 5% of subsequent premiums, and $200 on payment of the sum insured Calculate oV, 5V, 6V and 10V, that is, the gross premium policy values for this policy at times t = 0, 5, 6 and 10