Consider a semi-annual bond that has a par value of 100, a 15-year maturity, a 5% coupon rate. Monthly interest rate is 0.412%. (a) Calculate the annualized semi-annual compounding yield. (3 marks) (b) What is the price of the bond (without calculation)? And explain why you can determine the price of the bond without calculation? (4 marks) (c) Using answers from (b), calculate the modified duration of this bond. (3 marks) (d) Using answers from (b) and (c), suppose that the bond's yield to maturity decreases to 3.5%. How much will the bond price increase by applying the duration rule? (5 marks) (e) Do you agree with the following statement, and explain why? (5 marks) "If two bonds have the same duration, then the percentage change in price of the two bonds will be the same for a given change in interest rates." (f) Discuss the problems with the traditional bond pricing approach by using the yield to maturity. (300 words Maximum) (7 Marks)