This question is worth 10 marks in total. This is a written calculation question, and you should perform the necessary calculations/working on paper to later be scanned and uploaded. Start a new page for this question. For dollar amounts, give your answer to the nearest cent. For interest rates, give our answer as a percentage rounded to 2 decimal places.

If any parts of the question use values from earlier parts, use the EXACT values from earlier parts.

a) Explain the relationship between the yield to maturity of a par bond and its coupon rate. (1 mark)

Duncan recently completed ACST1001 and is hoping to apply what he has learned to start investing.

Duncan is interested in a $1,000 18-year bond paying half-yearly coupons with a coupon rate of 7.5%. The yield to maturity for such bonds is 8% p.a. compounding half-yearly.

b) Calculate the fair price Duncan should pay for one such bond, given the market conditions described above. (2 marks)

c) Suppose that 6 months after he initially purchases this bond, immediately after receiving the coupon on that date, Duncan decides to sell his bond to his friend Ian. Ian pays a price that yields 7% p.a. effective. Calculate the price Ian paid, ignoring any other costs (such as brokerage). (2 marks)

d) Calculate the return on Duncans 6 month investment, expressed as a percentage. (1 mark)