$6.(20$ points$)$ The market value, duration, and convexity of a bank's assets and liabilities are given:

Asset Value $$100$M$,$ Asset Duration $6,$ Asset Convexity $40$

Liabilities Value $$50$M$,$ Liabilities Duration $2,$ Liabilities Convexity $5$

$($Use weighted average of conexities to get convexity of bank's net equity$)$

$($c$)$ What is the convexity of the bank's net equity?

$($d$)$ Using duration and$/$or dollar duration alone $($i$.$e$.,$ not convexity$),$ approximate the change in the value of the bank's net equity if all zero rates rise by $50$ basis points.