Given the following information for an insurance company that writes $24-$month term policies:

All policies within each group have the same effective date.

$($a$)$ Calculate the earned car$-$years for calendar year $2011.$

$($b$)$ Calculate the earned car$-$years for policy year $2010$ evaluated as of December $31,2010$ and as of

December $31,2011.$

$($c$)$ Assume Policy Group B cancels on January $1,2011.$ Calculate the $2010$ policy year written car$-$

years evaluated as of December $31,2010$ and as of December $31,2011$ for Policy Group B$.$

$($d$)$ Assume Policy Group B cancels on July $1,2011.$ Calculate the $2010$ and $2011$ calendar year

written car$-$years for Policy Group B$.$