Problem $16-24($Algo$)$

A newly issued bond has a maturity of $10$ years and pays a $7\mathrm{.}5\%$ coupon rate $($with coupon payments coming once annually$).$ The bond

sells at par value.

Required:

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

b$.$ Find the actual price of the bond assuming that its yield to maturity immediately increases from $7\mathrm{.}5\%$ to $8\mathrm{.}5\%($with maturity still $10$

years$).$ Assume a par value of $100.$

c$.$ What price would be predicted by the modified duration rule $\frac{P}{P}=-D*y?$ What is the percentage error of that rule?

d$.$ What price would be predicted by the modified duration$-$with$-$convexity rule $\frac{P}{P}=-D^{*}y+\frac{1}{2}$ Convexity $(y{)}^2?$ What is

the percentage error of that rule?

Complete this question by entering your answers in the tabs below.

Required B

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

Note: Round "Convexity" to $3$ decimal places and "Duration" to $2$ decimal places.