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 $8\%.$

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 bond's yield to maturity increases to $9\%.$Are your conclusions about the accuracy of the two rules consistent with the parts $($a$)-($d$)$

PLEASE ONLY USE AND SHOWN WORK$/$FORMULAS IN EXCEL!!!