You are looking at options on Ravenclaw Corporation with $13$ months until expiration and a strike price of $$50.$ The risk free rate for maturities between $1$ and $13$ months is $2\mathrm{.}5\%($annualized with continuous compounding$).$ The firm is expected to pay a dividend of $$1\mathrm{.}20$ each quarter over the next $13$ months $($i$.$e$.$ a $$1\mathrm{.}20$ dividend in $3,6,9$ and $12$ months$),$ and the current stock price is $$48\mathrm{.}11.$ The price of the call option is $$3\mathrm{.}14$ and the put option is $$4\mathrm{.}79.$ Find the arbitrage trade given these prices and show the profit for each contract. $($Hint: use put$-$call parity with dividends$)$