(a) A company has decided to use bonds to finance a liability of $20,000 that must be re-paid using two payments. The first payment of $5000 must be made at the end of 6.75 years and the second payment of $15,000 must be made at the end of 8 years. There are currently three bonds in the market that are suitable to immunize these payments, Bond 1 which is a five-year pure discount bond with a face value of $1000, Bond 2 which is an eleven-year pure discount bond issued one year ago with a face value of $1500 and Bond 3 which is a seven-year pure discount bond issued three months ago with a present value of $594.83. Given that the yield to maturity in the bond market is 8%, determine:

(i) two separate portfolio strategies that will allow the company to immunize each liability payment. [8 marks]

(ii) for each of the portfolio strategies computed in Part 3(a)(i) above, the number of units the company should buy in each bond. [6 marks]