Consider a $16-$year, $9$ percent annual coupon bond with a face value of $$1,000.$ The bond is

trading $$t a market yield to maturity of $8$ percent.

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

b$)$ If the market yield to maturity increases to $8\mathrm{.}5$ 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 $0\mathrm{.}5$ percent increases in interest rates?