Consider a $$1,000$ par value bond with an $8\mathrm{.}5\%$ coupon rate and $15$ years remaining until

maturity. Interest is paid semiannually.

a$.$ What is the value of this bond if the required rate of return is $8\mathrm{.}5\%?$

b$.$ What would be the new value of the bond if the required rate of return suddenly

increased $($with no time elapsing$)$ to $11\mathrm{.}5\%?$

c$.$ Ignore the change in part $($b$).$ What would be the new value of the bond if the required

rate of return suddenly decreased $($with no time elapsing$)$ to $5\mathrm{.}5\%?$