What is the value of a derivative that pays off $$300$ in $6$ months if an index is less than $900$ and zero otherwise? Assume that the current level of the index is $920,$ the risk$-$free rate is $8\%$ per annum, the dividend yield on the index is $3\%$ per annum, and the volatility of the index is $20\%.$

$($a$)41\mathrm{.}08$

$($b$)68\mathrm{.}71$

$($c$)95\mathrm{.}33$

$($d$)114\mathrm{.}39$