(OLD SOA 51). 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 convertible semiannually; and a one-year bond with face amount of 1,000, a 5\% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually How much of each bond should Joe purchase in order to exactly (absolutely) match the liabilities