With well drawn diagrams explane the model on profit margin questions

Question 3.32 A special endowment policy pays a sum assured of 20,000 to a life who is currently aged exactly 57 after three years or at the end of the year of earlier death. Annual reversionary bonuses are declared at the end of each policy year, and a terminal bonus is payable at maturity only. Policies may be surrendered only at the end of each policy year. On surrender, the policyholder receives a return of premiums with interest calculated at the rate of 3% per annum. A level premium of $8,000 is paid at the start of each year. The premium basis is as follows: Interest: 7% per annum Mortality: AM92 Select Surrender rates: 15% of all policies in force at the end of year 1 5% of all policies in force at the end of year 2 Reversionary bonuses: 6% per annum compound . Terminal bonus: 10% of all other benefits payable at maturity Expenses: Initial $500 Renewal (30 at start of year 2 $35 at start of year 3 Termination {100 per termination (death, surrender or maturity) Reserves: Net premium reserves, using AM92 Ultimate mortality and 4% per annum interest. (i) Calculate the profit signature for this policy according to the premium basis. [14] (ii) Explain briefly whether you think the company expects to declare the bonus rates it has assumed in its premium basis, assuming all the other assumptions in the basis are realistic. [2]Question 3.31 Craig, aged 40, buys a four-year unit-linked endowment policy under which level annual premiums of f1,000 are payable. 75% of the first premium and 105% of each subsequent premium is invested in units. There is a bid/offer spread in unit values, the bid price being 95% of the offer price. A fund management charge of 0.75% of the value of the policyholder's fund is deducted at the end of each policy year. The death benefit, which is payable at the end of the year of death, is $3,000 or the bid value of the units if greater. The maturity value is equal to the bid value of the units. The insurance company incurs expenses of $150 at the start of the first year, $75 at the start of the second year, and f25 at the start of each of the third and fourth years. The rate of mortality is assumed to be 0.01 at each age and withdrawals may be ignored. (i) Assuming that the growth in the unit value is 5% pa and that the insurance company holds unit reserves equal to the value of units and zero non-unit reserves, calculate the profit emerging in each policy year. [10] (ii) Calculate the revised profit emerging each year assuming that the office sets up non-unit reserves to ensure that the profit emerging in the second and subsequent policy years is non-negative. Non-unit reserves are assumed to cam interest at 5% pa. [9]