A $30-$year$-$maturity bond making annual coupon payments with a coupon rate of $11\mathrm{.}2\%$ has duration of $11\mathrm{.}63$ years and convexity of $195\mathrm{.}34.$ The bond currently sells at a yield to maturity of $8\%.$Required:a$.$ Find 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$-1.$ What is the percent error for each rule?d$-2.$ What do you conclude about the accuracy of the two rules?e$-1.$ Find the price of the bond if its yield to maturity increases to $9\%.$e$-2.$ What price would be predicted by the duration rule?e$-3.$ What price would be predicted by the duration$-$with$-$convexity rule?e$-4.$ What is the percent error for each rule?e$-5.$ Are your conclusions about the accuracy of the two rules consistent with parts $($a$)($d$)?$