Problem $16-24($Algo$)$

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:

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 $8\mathrm{.}5\%$ to $9\mathrm{.}5\%($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?

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.

$\backslash$table$[[$Convexity$,,],[$Duration$,,$years$]]$

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 $100.$

Note: Round your answer to $2$ decimal places.

Show less A

Actual price of the bond

What price would be predicted by the modified duration rule $2$ formula $103.$mmI What is the percentage error of that rule?

Note: Negative answers should be indicated by a minus sign. Round your answers to $2$ decimal places.

$\backslash$table$[[$Percentage price change,$\%$