$(8$ points$)$ Assume that you have a portfolio with the following key rate $01$ s $.\backslash$begin$\{$tabular$\}\{$cccc$\}2-$year & $5-$year & $10-$year & $30-$year $\backslash \backslash 24$ & $58$ & $78$ & $110\backslash$end$\{$tabular$\}$ And you want to hedge it using $2-,5-,10-,$ and $30-$year bonds with $\backslash (\backslash$$ $100\backslash )$ face values. However, you cannot find $5-$ and $10-$year par bonds. The key rate $01$ s of these bonds are given below. How many bonds do you need to buy$/$sell$?$ Keep $4$ decimals for all the numbers, e$.$g$.,0\mathrm{.}3999,2\mathrm{.}9999\backslash \%$ for percentage. $\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}\backslash$hline & $2-$year key & $5-$year key & $10-$year key & $30-$year key $\backslash \backslash \backslash$hline $2-$year bond & $0\mathrm{.}04$ & $0$ & $0$ & $0\backslash \backslash \backslash$hline $5-$year bond & $0\mathrm{.}075$ & $0\mathrm{.}06$ & $0$ & $0\backslash \backslash \backslash$hline $10-$year bond & $0\mathrm{.}128$ & $0\mathrm{.}088$ & $0\mathrm{.}105$ & $0\backslash \backslash \backslash$hline $30-$year bond & $0$ & $0$ & $0$ & $0\mathrm{.}249\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}$