An investor wants to find the duration of$$ a$($n$)15-$year, $5\%$ semiannual$$ pay, noncallable bond$$ that's currently priced in the market at $$$$477\mathrm{.}65,$ to yield $13\%.$ Using a $100$ basis point change in$$ yield, find the effective duration of this bond $($Hint$$: use Equation$11\mathrm{.}11).$

$1.$ The new price of the bond if the market interest rate decreases by $100$ basis points$($or $1\%)$ is $???($Round to the nearest$$ cent.$)$

$2.$ The new price of the bond if the market interest rate increases by $100$ basis points$($or $1\%)$ is $???($Round to the nearest$$ cent.$)$

$3.$Find the effective duration of this bond: $???$