ANSWER: 0.93809 of the first bond and 0.97561 of the second bond

please show and explain work

The following information applies to Problems 56.4 - 56.6 Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments: a 6-month bond with face amount of 1,000, a 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convert- ible semiannually, and a one-year bond with face amount of 1,000, a 5% nominal annual coupon 56 FULL IMMUNIZATION AND DEDICATION 543 rate convertible semiannually, and a 7% nominal annual yield rate convert- ible semiannually. Problem 56.4 How much of each bond should Joe purchase in order to exactly (absolutely) match the liabilities