A man aged 40 purchases a 20-year endowment insurance with a sum insured of 200000 payable at the end of the year of the death or on survival to age 60, whichever occurs first. Premium are paid annually at the beginning of the year. The insurance company use the following basis for all calculation. Mortality model: the standard select survival model. Interest rate: 5% year effective Expenses12% of the first premium, 5% of subsequent premiums, plus $150 on payment of sum insured.

a. Draw a picture for the problem.

b. Calculate the gross premium.

c. Calculate the gross premium policy value at t=5