A newly issued bond has a maturity of $10$ years and pays a $8\mathrm{.}5\%$ coupon rate $($with coupon payments coming once annually$).$ The bond sells at par value.

Required:

What are the convexity and the duration of the bond? Use the formula for convexity in footnote $7.$

Find the actual price of the bond assuming that its yield to maturity immediately increases from $8\mathrm{.}5\%$ to $9\mathrm{.}5\%($with maturity still $10$ years$).$ Assume a par value of $100.$

What price would be predicted by the modified duration rule $\backslash$Delta PP$=$D$*\backslash$Delta y$?$

What is the percentage error of that rule?

What price would be predicted by the modified duration$-$with$-$convexity rule $\backslash$Delta PP$=$D$*\backslash$Delta y$+12\backslash$times Convexity$\backslash$times $(\backslash$Delta y$)2?$

What is the percentage error of that rule?