A $30-$year maturity bond making annual coupon payments with a coupon rate of $12\%$ has Macaulay$$s duration of $11\mathrm{.}54$ years and convexity of $192\mathrm{.}4.$ The bond currently sells at a yield to maturity of $8\%.$ Use excel and show formulas for all of the below questions. A$)$What is the price of the bond if its yield to maturity falls to $7\%.$ B$)$What price would be predicted by the duration rule? C$)$ what price would be predicted by the duration$-$with$-$convexity rule? D$)$What is the percent error for each rule? What do you conclude about the accuracy of the two rules? E$)$ Repeat your analysis if the bonds yield to maturity increases to $9\%.$ Are your conclusions about the accuracy of the two rules consistent with the pearts $($a$)-($d$)?$