there is a part b that is seperated because of a page break. please answer with handwritten formula work only, no spreadsheet/excel, thank you

Problem 4. ABC 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. (i) A 6-month bond with face value of 1,000, a r = 8% nominal annual coupon rate compounded semiannually, and a nominal annual yield rate of i = 6%. (ii) A one-year bond with face value of 1000, a coupon rate of r = 5% compounded semiannu- ally, and a nominal annual yield rate of i = 7%. a. How much of each bond should ABC purchase in order to exactly match the liabilities? 1 b. What is ABC's total cost of purchasing the bonds required to exactly match the liabilities