Consider a $$1,000\mathrm{ 1}0-$year bond that pays a $2\mathrm{.}5\%$ annual coupon.

$($a$)$ Compute the current price and the duration of this bond, given that the required interest rate is $2\mathrm{.}5\%.$  

$($b$)$ Suppose that the interest rate jumps to $3\%.$ What is the percent price change in the bond? Use the approximate formula based on Duration that we learned in class.

$($c$)$ What is the new price level of the bond?