stion $3$

$10pts$

options on a stock are available with strike prices of $$15,$$$17\mathrm{.}5,$ and $$20$ and expiration $s$ in three months. Their prices are $$4,$$$2,$ and $$0\mathrm{.}5$ respectively. An investor can create a erfly spread by buying call options with strike prices of $$15$ and $$20$ and selling two call ons with strike prices of $$17\mathrm{.}50.$

What is the initial investment required for this butterfly spread?

What is the profit if the final stock price $S(T)=$$$11\mathrm{.}00?$

What is the profit if $S(T)=$$$16\mathrm{.}00?$

$4.$ What is the profit if $S(T)=$$$18\mathrm{.}00?$

$5.$ What is the profit if $S(T)=$$$22\mathrm{.}00?$

Enter your answer without the dollar sign, with $2$ decimals, such as $2\mathrm{.}30$; enter losses as negative numbers.$)$