Nathan purchased a 5-year Treasury bond with a coupon rate of j2 = 3.50% p.a. and a face value of $100 that matures at par. Coupons can be reinvested at j2 = 3.2% p.a. for the first four and a half years. a. [2 marks] Calculate Nathans purchase price for this bond at a yield rate of j2 = 3.1% p.a. (rounded to three decimal places). b. [4 marks] Assume that Nathan held this bond to maturity to earn a total realised compound yield of j2 = 3.13% p.a. Based on your result from part a, calculate the reinvestment rate for the last half year. Give your answer in j2 form, rounded to two decimal places. c. [3 marks] Assume that Nathan held this bond for 2 years and sold it for a yield of j2 = 3.8% p.a. Based on your result from part a, calculate the holding period yield in j2 form, rounded to two decimal places. Include in your answer a cash flow diagram, drawn from Nathans perspective, that models the purchase and sale of the bond. d. [2 marks] Without any further calculations, explain how the holding period yield will change if the sale yield is lower than j2 = 3.8% p.a. e. [4 marks] Assume that this bond is subject to a 30% tax on interest and capital gains. Recalculate the price Nathan paid (in part a) if the net yield rate is j2 = 3% p.a. and all tax payments (interest tax payments and capital gains tax payment) are delayed by one year from when taxable cash flows occur. Round your result to three decimal places. Accompany your answer with a cash flow diagram, from Nathans perspective, that models this scenario.