do not use excel - show working out

a) A 20-year bond with a face value of $1,000 will mature in 8 years. The bond pays semi-annual coupons at 5% p.a. compounding half-yearly. Mia wants to purchase the bond at a price which gives her a yield to maturity of 6% p.a. compounding half-yearly. Calculate the maximum price Mia should pay for the bond. (Round your answer to the nearest cent) (3 marks)

b)A zero-coupon bond has a face value of $1,000 and will mature on 1 July 2025. Aiden purchased the bond on 1 January 2019 at a price which gave him a yield to maturity of 8% p.a. compounding half-yearly.

i) Calculate the price Aiden paid for the bond. (Round your answer to the nearest cent) (2 marks)

ii) Aiden held the bond for 2 years and sold it to Helen on 1 January 2021. Helen paid a price which gave her a yield to maturity of 6% p.a. compounded half-yearly. Calculate the price Helen paid for the bond. (Round your answer to the nearest cent) (2 marks)

iii) Calculate the total holding period return earned by Aiden over the period he held the bond. (Round your answer to the nearest 0.01%) (2 marks)