$(1)(25$ pts$)$ A corporate bond has a modified duration of $6\mathrm{.}800$ and an approximate convexity of $33\mathrm{.}750.$ Assume that changes in its credit rating by the rating agencies causes the bond$$s yield spread to increase or decrease. Please answer the following questions.

$($a$)$ What would be the price impact of a $50$bps increase in its spread over the benchmark, ignoring convexity? Be sure to indicate if it is a price increase or decrease.

$($b$)$ What would be the price impact of a $75$ bps decrease in its spread over the benchmark, ignoring convexity. Be sure to indicate if it is a price increase or decrease.

$($c$)$ What would be the price impact of a $175$ bps increase in spread over the benchmark. Include the convexity correction.

$($d$)$ What would be the price impact of a $175$ bps decrease in spread over the benchmark. Include the convexity correction.