Question 1 [12 marks] On the 11th of April 2015, Alfred is considering purchasing two bonds, B and C, with the following characteristics. Bond B pays coupon at j2 = 2% p.a., with face value of 100 and matures on the 11th of October 2017. Assume the coupon due on the 11th of April 2015 has already been paid and the next coupon payment is due on the 11th of October 2015. Bond C pays coupon at j2 = 3% p.a., with face value of 100 and matures on the 11th of November 2017. Assume the next coupon is due on the 11th of May 2015.

Note: assume the yield on both bonds is j2 = 4% p.a.

a. [6 marks] Determine the price of both bonds now (11.iv.15).

b. [3 marks] Determine the duration and modified duration of both bonds in half-years as at 11.iv.15.

c. [3 marks] Alfred has been rather foolish and incurred a liability of $3 000 000 due in 4.91 half-years (from 11.iv.15). Assist Alfred by constructing a portfolio, comprised of bonds B and C, that matches the duration of Alfred's liability.