BKM Ch$11$ problem $26$

A $30-$year maturity bond making annual coupon payments with a coupon rate of $12\%$ has $($Macauley$)$ duration of

$11\mathrm{.}54$ years and convexity of $192\mathrm{.}4.$ The bond currently sells at a yield to maturity of $8\%.$

a$)$ Find the price of the bond if ytm falls to $7\%($use financial calculator or spreadsheet$).$

b$)$ What price would be predicted using duration only?

c$)$ What price would be predicted using duration and convexity?

d$)$ What is the error $($in $\%)$ for each rule? What do you conclude about accuracy of the two rules?

e$)$ Repeat the analysis with yields rising to $9\%.$ Do your conclusions about accuracy hold up$?$