Help in solving the following questions.

a- -m" (i) Prove that (la), [3] A government bond pays a coupon half-yearly in arrears of $10 per annum. It is to be redeemed at par in exactly ten years. The gross redemption yield from the bond is 6% per annum convertible half-yearly. (ii) Calculate the duration of the bond in years. [8] (iii) Explain why the duration of the bond would be longer if the coupon rate were $8 per annum instead of $10 per annum. [2] [Total 13]A life insurance company issues a 20-year with-profit endowment assurance policy to Russell, aged 40. The sum assured of $20,000 plus declared reversionary bonuses is payable immediately on death, or on survival to the end of the term. (i) Calculate the quarterly premium payable by Russell throughout the term of the policy if the office assumes that future reversionary bonuses will be declared at the rate of 1.92308% of the sum assured, compounded and vesting at the end of each policy year on the following basis: Mortality: AM92 Select Interest: 6% pa Initial expenses: 114% of the first premium and 2.5% of the basic sum assured Renewal expenses: 4% of each quarterly premium, excluding the first [8] (ii) The life office values its with-profit business using the net premium method, assuming an interest rate of 4% pa and AM92 Ultimate mortality. Calculate the prospective reserve for Russell's contract described above just before the 13th quarterly premium is payable, given that the total reversionary bonus declared up to that time is $600. [5] [Total 13]QUESTION TWO (a) Define elasticity of supply and briefly explain any five factors that influence the elasticity of supply. (10 marks) (b) Explain why elasticity of supply for agricultural commodities is low. (6 marks)