Please answer the questions below appropriately.

An institution has a liability to pay $15,000 per annum, half-yearly in arrears, forever. (i) Calculate the present value and volatility of the liability at 8% pa effective. [6] (ii) Calculate the duration of the liability at 8% pa effective. [1] The following two stocks are available for investment: (A) A special 5-year stock, redeemable at par, that pays a coupon of 5 per 100 nominal at the end of the first year rising, by 2% pa compound, to 5 x1.02# at the end of the fifth year. (B) An n-year zero-coupon bond, redeemable at par. The institution chooses to invest equal amounts of cash in Stock A and Stock B. (iii) If the institution requires that the duration of the assets must equal the duration of the liabilities, show that n, the term of the zero-coupon bond, must equal 22 years if interest rates are 8% pa effective. [8] (iv) Without doing any further calculations, explain whether the institution has managed to implement an immunisation strategy. [2] [Total 17]Consider each of the symbols listed below: {a} msfy {II} F; in} .1, {d} I; is} 711; Explain carefully the meaning of each of these symbols and calculate the value of each, assuming that: a {I} is subject to a constant force of mortality ofl pit - {y} is subject to a constant force of mortality ofz pa - the lives are independent with respect to mortality c the force of interest is Emmi [I 3]