Consider a$($n$)$ Five$-$year, $12$ percent annual coupon bond with a face value of $$1,000.$ The bond is trading at a rate of $9$ 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$.,32\mathrm{.}16))$