A liability fo 1000 is due 6 months from now as well as another 1000 is due one year from now. There're two available instruments:
a. A 6 month bond with face amount of 1000, 8% nominal couon convertible semi annually, yielding 6% nominal converted semi annually.
b. A one year bond with face amount of 1000 a 5% nominal coupon convertible semi annually, yielding 7% semi annually
1. How much of each bond should be purchased to exactly match the liabilities?
2. What is the total cost of purchasing the bonds required to exactly match the liabilities?
3. What is the annual effective yield rate for the two investments required to match the liabilities?