$2.$ Consider a semi$-$ annual coupon payment bond selling at par $($$$1000)$ with a coupon rate of $4\%$ and $3$ years to maturity.

$($a$)$ Calculate the percentage change in the bond price if the yield increases from $4\%$ to $5\%.$

$($b$)$ Calculate the Modified Duration for the bond.

$($c$)$ Calculate the Macaulay Duration for the bond.

$($d$)$ Calculate the Convexity for the bond.

$($e$)$ Calculate the percentage change in bond price based on duration and convexity if the yield increases from $4\%$ to $5\%?$