- Please write all answers that involve percentages as such (e.g. 7.2456\%), and not as decimals (0.072456). - When necessary, please give answers to four decimal places. Question 1 The current discount rate, assuming a 360 day year, on a 90 -day bill is 3.5 percent. The face value is ZAR1 million. (i) What is the price of the bill? [3 marks] (ii) If the discount rate increases by one basis point to 3.51 percent, what is the change in the price of the bill? [3 marks] (iii) If the discount rate decreases by one basis point to 3.49 percent, what is the change in the price of the bill? [3 marks] Question 2 The cash prices of 6-month and 1-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every 6 months currently sells for $94.84. A 2-year bond that will pay coupons of $5 every 6 months currently sells for $97.12. Calculate the 6-month, 1-year, 1.5-year, and 2-year zero rates. Question 3 Portfolio A consists of a 1-year zero-coupon bond with face value of R2 million and a 10-year zero-coupon bond with a face value of R6 million. Portfolio B consists of a 5.95year zero-coupon bond with a face value of R5 million. The current yield on all bonds is 10% per annum. (i) Show that both portfolios have the same duration. [5 marks] (ii) Show that the percentage changes in the value of the two portfolios for a 0.1% per annum increase in yields are the same. [5 marks] (iii) What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields? Comment on your results. [ 8 marks]