answer a$-$e A $30-$ year$-$maturity bond making annual coupon payments with a coupon rate of $12\%$ has duration of $11\mathrm{.}54$ years and convexity of

$192\mathrm{.}4.$ The bond currently sells at a yield to maturity of $8\%.$

a$.$ Use a financial calculator or spreadsheet to 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?

$d.$ 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 parts $(a)-(d)?$