An insurer sells a 20-year mortgage protection product. The sum assured, which is payable at the end of the policy year of death, is (550,000 (t 1) 25,000) during policy year t . The policy is purchased by level premiums payable annually in advance as long as the policy remains in force. In pricing and valuing the policy the insurer assumes the following: Basis: Mortality AM92 Select Interest 4% p.a. effective Initial Expenses 200 Regular Expenses 3% of all premiums received Initial Commission 25% of the annual premium Regular Commission 2% of all premiums received Consider such policies sold to individuals aged 30 exact. (a) Calculate the annual gross-premium payable for such policies using the principle of equivalence. (b) Calculate the net-premium reserve for such policies still in force at the end of their first and second policy years. The insurer issued 1,000 such policies to lives aged 30 exact. Two policies went out of force due to deaths during the first policy year and no policy went out of force due to deaths during the second policy year. No policy lapsed during the first two policy years. For calculations of annual mortality profits on such policies, the insurer uses a net-premium reserving basis. (c) Calculate the mortality profit, or loss, to the insurer in respect of the first two policy years. (d) Calculate the gross-premium prospective reserve at the end of the 17th policy year assuming the policy is then still in force.