A $18-$year bond pays a semi$-$annual coupon of $4\%($compounded semi$-$annually$),$ on a face value of $$1000.$ The bond's yield is $2\%$ compounded semi$-$

annually.

$($a$)$ Determine the price of the bond. Express your answer in dollars, to the nearest cent.

Price $=$$

$($b$)$ Determine the derivative of the bond's price with respect to $($per$-$period$)$ yield, at its current yield. Express your answer in dollars, to the nearest cent.

Derivative $=$$

$($c$)$ Determine the bond's duration. Express your answer in years, to two decimal places. Please use the rounded answers from $($a$)$ and $($b$)$ in your

calculation.

Duration $=$

Years