Problem $3-34($LG $3-4)$

Consider a$($n$)$ Ten$-$year, $11\mathrm{.}5$ percent annual coupon bond with a face value of $$1,000.$ The bond is trading at a rate of $8\mathrm{.}5$ percent.

a$.$ What is the price of the bond?

b$.$ If the rate of interest increases $1$ percent, what will be the bond's new price?

c$.$ Using your answers to parts $($a$)$ and $($b$),$ what is the percentage change in the bond's price as a result of the $1$ percent increase in interest rates? $($Negative value should be indicated by a minus sign.$)$

d$.$ Repeat parts $($b$)$ and $($c$)$ assuming a $1$ percent decrease in interest rates.

$($For all requirements, do not round intermediate calculations. Round your answers to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$

$\backslash$table$[[,,],[$a$.,$Price of the bond,,$],[$b$.,$Bond's new price,,$],[$c$.,$Percentage change,,$\%,],[$d$.,$Bond's new price,,$],[,$Percentage change,,$\%$