An American call option on a stock has a strike price of $85$ and expires in $5$ months. You are given:

$($i$)$ The risk free rate is $4\%,$

$($it$)$ A dividend of $1\mathrm{.}50$ is payable at the end of today, and another dividend of $1\mathrm{.}50$ is payable in $3$ months.

$($iii$)$ The current price of the stock is $100.$

$($iv$)$ A kuropean put opion with a strike price of $85$ whch expires in $3$ inonths costs $0\mathrm{.}82.$

Could it be rational to exercise the option immediately, before the dividend is paid?