Suppose the 0.5-year zero rate is 6% and the 1-year zero rate is 8%. Consider a 1-year, semi-annual pay, fixed-for-floating interest rate swap between risk-free borrowers. a) What is the swap rate that will make this swap worth zero? b) If the nominal face value of the swap is $100. What is the is the dollar duration of the fixed-rate bond and the FRN involved in the swap? c) Compute the dollar duration of the swap by taking the difference between dollar duration of the fixed rate bond and that of the FRN. d) Your liabilities have a market value of $100,000 and a duration of 3. Your assets have a market value of $100,000 and a duration of 5. Assuming that you are a risk-free borrower and can long or short the swap above. What position (long or short) and how many of the above swap contracts you would have to enter in order to immunize yourself from parallel shifts in interest rates. Ignore convexity.