On 1 June, 2019, immediately after payment of the interest due that day, Tim Shaw bought two bonds each with a face value of $100,000 and a coupon rate of 8% p.a., paid half-yearly. The first bond will mature on 1 December 2021 and the second bond will mature on 1 December 2025. At the date of purchase, both bonds were selling at par.

Since the date of purchase, yields on bonds have risen by 2% p.a., compounded half-yearly. Tim now intends to sell the bonds and put a deposit on a house.

a. Calculate the price he will receive from each bond if he sells on 1 September, 2019 at the new yield. (Hint: There are 92 days from 1 June, 2019 to 1 September, 2019, and 183 days from 1 June, 2019 to 1 December, 2019 – in both cases, ignoring the first day and including the last day of the period.) (6 marks)

b. Explain the relative price movements in the two bonds, as evidenced in your answer to part a. above. (4 marks)