You are the reserving actuary for a company that sells three-year immediate term annuity to 65 year old male retirees. This demographic experiences 10 per mille mortality in any policy years. The annuities are paid at a rate of 40% of the initial premium per annum and payments are made at the end of the year, if the policyholder survives. The investment returns based on the investment strategy developed by the company is expected to deliver 10% per annum return for the next three years. Actual internal expenses may be assumed to be $200 as initial expense, $50 on-going expense per policy. Expenses are assumed to occur at the end of a policy year in which they are incurred. There is no initial commission payable to the brokers as the service payments are covered by a separate fee agreements between policyholders and brokers. (i) State what assumptions are required to demonstrate the reserving methodology does not affect total profit. Prove that the profit is independent of the reserving basis under your stated assumptions. [4] Local regulation requires the discount rate for this line of business to be 10% per annum for the next three years. There are large taxation penalties for early withdrawal. Assuming your reserving basis is on a best estimate basis, and stating any further assumptions you require, draw and calculate the profit signature for a policy of $50,000 premium. For the purpose of answering this question, you may ignore the capital requirements. [5] Hint: You need to show appropriate cashflows and calculate profit signature based on the cashflows you have constructed.