A $4-$yr $6\%$ coupon bond has a face value of $1,000,000,$ current market value of $1,041,420\mathrm{.}09,$ dollar duration of $3,683,543\mathrm{.}77,$ and dollar convexity of $15,633,495\mathrm{.}44.$ Suppose a long position in the $6\%,4-$year bond is to be duration matched with $1\mathrm{.}5-$year and $3\mathrm{.}5-$year zeros. Answer the following questions for this immunization. A$.$ What are the market values of the zeros used in this duration matching? $(0\mathrm{.}50)$ B$.$ What are the dollar durations of the zeros used in this duration matching? $(0\mathrm{.}50)$ C$.$ How many of the two zeros are required to immunize the $6\%,4-$year bond? $(0\mathrm{.}50)$ D$.$ Using duration approximation, what is the change in value of both the $6\%$ bond and the portfolio used to immunize the bond for $25$ basis points change interest rate? E$.$ What is the actual change in the value of the portfolio used to immunize the bond if the $3\mathrm{.}5$ year zero rate changes by $20$ basis points while $1\mathrm{.}5$ and $2-$year zero rates change by $27$ basis points? $(0\mathrm{.}75)$

$3.$ Consider the following rates:

A$.$ What are the dollar duration, duration, dollar convexity, and convexity of a newly$-$issued $2$year floating rate note? $(0\mathrm{.}50)$

B$.$ Suppose a fixed coupon bond with $2-$year maturity is to be issued at par. What would be the coupon rate on this bond? $(1\mathrm{.}25)$

C$.$ What would be the dollar duration and dollar convexity of the $2-$year fixed coupon par bond? $(1\mathrm{.}00)$

D$.$ If $\backslash (\backslash$$ $200\backslash )$ par of the $2-$year fixed coupon bond is used to issue a $\backslash (\backslash$$ $100\backslash )$ par floater and $\backslash (\backslash$$ $100\backslash )$ par inverse floater, what would be the duration and convexity of the inverse floater? $\backslash ((0\mathrm{.}50)\backslash )$