QUESTION 5. [(a. +b. +C. + d.i. + d.ii. + e. = 4. Marks)] | + 4 + 4 = 24 marks) + (f. = REC'NS = 2 On 15 December, 2020, Alan Chan bought a bond with a face value of $100,000, a coupon of 8% per annum, payable half-yearly and a yield to maturity of 6% per annum, compounded half-yearly. The most recent interest coupon payment was made to the seller on the morning of the purchase and the bond is due to mature on 15 December, 2022. REQUIRED: Answer each of the following parts. Show answers with the accuracy specified a. What price would Alan have paid for the bond? [Show answer correct to the nearer 11/17 b. Calculate the duration of the bond. [Show answer in half-years, correct to 4 decimal p. Calculate the convexity of the bond. [Show answer correct to 4 decimal places.] d. If, immediately after purchase, the yield to maturity falls to 5% per annum, compounded half-yearly, calculate the expected new bond price - separately, by each of the following two methods: i. Estimating the purchase price by the duration-with-convexity adjustment. ii. The present value of future cash flows under the bond, discounted by the new yield. [Show each answer, i. and ii. above, correct to the nearer cent.) e. Following the fall in yield in d., Alan plans to sell the bond on 15 February, 2021. What price would he expect to get in an efficient market? [HINT: Alan will have held the bond for 62 days up to the