SOLVE ONLY PARTS III) AND IV), USING FORMULAS, NO TABLES, CORRECT ANSWERS ARE FOR PART III) i^2 = 5.5% pa AND FOR PART IV) PV = £1,146.13, GIVEN THAT ANSWERS FOR PART I) IS A(T) = EXP(0.03T + 0.0025T^2) FOR 0 6 (i) (ii) Derive, and simplify as far as possible, expressions in terms of t for the accumulated amount at time t of an investment of £1 made at time t = 0. You should derive separate expressions for both sub-intervals. Using the result in part (i), calculate the value at time t = 3 of a payment of £2,000 made at time t = 7. (iii) (iv) Calculate, to the nearest 0.1%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii). A continuous payment stream, under which the rate of payment per annum at time t is p(t) = 500e-0.01t, is invested between t = 10 and t = 15. Using the result in part (i), calculate the present value (at time t = 0) of this investment.