a) The value of a consol bond is given by the formula below: PV=(1+r)C+(1+r)2C+(1+r)3C+ Show that this formula can be simplified to: PV=rc Hence, calculate the value of a consol bond that pays K12,000 per year and was bought at a discount rate of 8%. (5 marks) b) Calculate the Macaulay duration and the modified duration of a three-year bond with a face value of K1,00 that pays a 11% coupon semi-annually and has a yield to maturity of 6%. Interpret your answers. (15 marks)