At the end of May 2021 a US corporate bond has an annual coupon rate of 3%, a par (face) value of 1,000 and will mature in 4 years in May 2025. Market rates of interest are currently 2%. (a) Using the data given above and assuming semi-annual coupons and a semiannual discount rate equal to 1%, calculate the value of the corporate bond. (4 marks) (b) Calculate the Macaulay duration of the corporate bond described above assuming annual coupons and discount rate. (5 marks) (c) Explain why there is an inverse relationship between the price of a bond and market rates of interest. (5 marks) (d) Explain Macaulay duration and describe the main characteristics of Macaulay duration in relation to bonds. (6 marks) (e) Explain modified duration and explain the limitations of using this measure