The following information applies to questions 1 thru 3. 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.

1). How much of each bond should Joe purchase in order to exactly (absolutely) match the liabilities?

2). What is Joes total cost of purchasing the bonds required to exactly (absolutely) match the liabilities?

3). What is the annual effective yield rate for investment in the bonds required to exactly (absolutely) match the liabilities?