I need your help microeconomics questions

Initial expenses: f1 25 Renewal expenses (associated with the payment of the second and each subsequent premium) f20 increased by 7% p.a. compound from the outset of the policy. Growth rate for units: 7% p.a. Interest rate for sterling fund: 4% p.a. (a) On this basis (i) construct a table showing the growth of the unit fund over the duration of the policy, and (fi) construct a table showing the growth of the sterling fund in the absence of reserves. (b) Hence determine the sterling reserves which should be held by the office to eliminate the sterling fund negative cash flows in the second and subsequent years of the policy's duration. (c) Consider the unit-linked policy described above. Suppose, however, that the growth rate for units will be 10% p.a., that the sterling fund interest rate will be 6% p.a., and that the inflationary growth rate for renewal expenses will be 4% p.a. (from the outset of the policy). (i) Construct a table showing the growth of the unit fund over the duration of the policy and (ii) Construct a table showing the growth of the sterling fund in the absence of reserves. (ini) Assuming that the office sets up the sterling fund reserves found above, determine the resulting sterling fund profit vector and signature. Find also the internal rate of return corresponding to the profit signature.(ii) the profit signature per policy sold if Sterling reserves are zeroised. (c) The office now wishes to make an allowance for surrenders. It assumes that, at the end of the first and the second policy years, 3% of the surviving policyholders will surrender (just before payment of the second and third annual premiums respectively.) Surrender values are equal to the value of the policyholder's units (after deduction of fund management charges), with a surrender penalty of f10. Calculate (i) the revised profit signature per policy sold, ignoring any need to maintain Sterling Reserves at the end of each year, (ii) the revised profit signature per policy sold if the Sterling Reserves are zeroised, and (iii) the net present value, at a risk discount rate of 15% per annum, of the revised profit signature per policy sold, assuming that the Sterling Reserves are zeroised. 4.3 (a) If a profit test for a unit-linked policy reveals negative cash flows in the second or any subsequent policy year, it is customary to eliminate these negative values by setting up sterling reserves at the end of each year. Describe briefly the technique ("zeroisation" ) by which these reserves are calculated. (b) An office issues a 3-year unit-linked policy with a yearly premium of 2500. The death benefit, payable at the end of the year of death, is 21.000 or the bid value of units if greater. The maturity value is the bid value of the units at maturity. 95% of each premium is invested in units at the offer price. The bid price of units is 95% of the offer price. Management charges of 2% of the bid value of the units are deducted at the end of each year (before payment of death and maturity claims). The office expects to incur expenses of 675 at the start of the first year and 225 at the start of each subsequent year. Using a profit testing analysis, calculate for a life aged 60 at entry (i) the expected profit in each of the 3 years per policy in force at the beginning of the year, (ii) the net present value at the issue date of the expected profit from one policy assuming a risk discount rate of 10% per annum. Assume that the unit fund grows at 8% per annum ( before deduction of management charges), that sterling reserves need not be maintained at the end of each year, and that the possibility of surrender may be ignored. The mortality of policyholders follows A1967-70 ultimate and sterling reserves earn interest at 6% per annum during each policy year. 4.4 If a profit test for a unit-linked policy reveals negative cash flows in the second or any sub- sequent policy year, it is customary to eliminate these negative values by setting up sterling reserves at the end of each year. Calculate the sterling reserves required at the end of each policy year, per policy then in force, for a 3- year policy for which the profit signature (with no allowance for sterling reserves at the end of each year) is (250, - 100, - 50), given that the rate of mortality is 0.01 per annum at each age and sterling reserves earn interest at 8% p.a. An office issues a unit-linked endowment assurance with annual premium 2400 and term five years to a life aged 60 who is subject to A 1967-70 ultimate mortality. The sum assured, payable at the end of year of death or at the maturity date, is the bid value of the units held, subject to a guaranteed minimum death benefit of 22.000. The allocation proportion is 70% for the first annual premium and 98% for all subsequent annual premiums. For units the bid/offer spread is 5% and the annual rate of management charge is 0.75%. In determining the sterling reserves necessary for the policy the office makes the following assumptions:4.1 A life office issues a three-year unit-linked endowment policy to a life aged exactly 60 The annual premium 3 22,000, payable at the start of each year. The allocation proportion is 30/ in year 1 and 97% thereafter. At the end of year of death during the term, the policy pays the higher of f 10,000 and the bid value of units allocated to the policy, after deduction of the fund management charge. A bonus of 2% of the (bid) value of the unit fund is payable at maturity. The life office makes the following assumptions in projecting future cash flows: Mortality A1967-70 ultimate Initial expenses: 6300 Renewal expenses: 450, incurred at the start of the second and the third years Fund management charge: 2% per annum, taken at the end of each year before payment of any benefits Sterling fund interest rate: 4% per annum Bid/offer spread: 6% Unit fund growth rate: 10% per annum. Construct tables to show the following: (i) the growth of the unit fund; (in the profit signature, assuming that no sterling reserves are held; (ii) the profit signature after taking into socount sterling reserves, given that the sterling reserves per policy are to be 236.48 before receipt of the premium due at time 1 year and 178.64 before receipt of the premium due at time ? years. In each case, indicate clearly how you calculate your table entries. Ignore the possibility of surrendera. 4.2 (a) In the context of profit-testing of unit-baked business, define the following terms briefly: (i) the Unit Fund, (in the Sterling Reserves, (ii) the profit vendor of a policy, (iv) the profit signature of a policy. (v) the risk discount rate, and (vi) zeroisation of Sterling Reserves. (b) A life office issues a large number of identical 4-year annual proc ium unit-linked endow- ment assurances to lives aged 65. According to the office's calculations, the profit vector per policy sold, ignoring withdrawals and assuming that no Sterling reserves are maintamed at the end of each year, is as follows ( f): 191.12 -111.45 -3.28 10.95 The office's mortality basis is A1937-70 ultimate, and Sterling Reserves earn interest at 5% per annum. Calculate (i) the profit signature per policy sold, ignoring am need to maintain Sterling Reserves at the end of each year, and