Assume that the Treasury yield curve is flat at 3% on a bond-equivalent basis (i.e., an investment of $100 receives a $3 interest payment at the end of the year). Utilize the duration and convexity calculator and answer the following (a) - (d). (a) Calculate the modified duration and the convexity of a 1-year zero coupon Treasury bond. (b) Calculate the modified duration and the convexity of a 5-year Treasury bond with a coupon rate of 4%. Assume the coupon is paid annually. (c) Suppose that you have a portfolio consisting of $100,000 invested in the 1-year bond in (a) and $250,000 invested in the 5-year bonds in (b). Using the approximation formula for price changes based on both duration and convexity, what will happen to the value of your portfolio if interest rates fall by 50 basis points (.0050)?

Be specific about the signs here and use + and - to respectively indicate gain and loss. Again, write your answers in unit of dollars. (d) Calculate the dollar duration of a 10-year fixed-for-floating interest rate swap with annual payments, a fixed rate of 3.25% on a bond-equivalent basis, and a floating payment based on the 1-year swap yield that resets annually. Report the result from the perspective of the floating rate payor.

Assume that: the swap is currently priced at par; it has notional principal of $1 million; and the swap yield curve is flat at 3.25% on a bond-equivalent basis.

Write your answer in unit of million dollars.