$[$Introductory Derivatives Sample Question $43]$ You are given:

$($i$)$ An investor short$-$sells a non$-$dividend paying stock that has a current price of $44$ per share.

$($ii$)$ This investor also writes a collar on this stock consisting of a $40-$strike European put option and a $50-$strike European call option. Both options expire in one year.

$($iii$)$ The prices of the options on this stock are:

$\backslash$table$[[$Strike Price,Call option,Put option$],[40,8\mathrm{.}42,2\mathrm{.}47],[50,3\mathrm{.}86,7\mathrm{.}42]]$

$($iv$)$ The continuously compounded risk$-$free interest rate is $5\%.$

$($v$)$ Assume there are no transaction costs.