The current stock price is $45.$ The stock is going to pay a dividend of $1$ after $3$ months. This

is the only dividend to be paid in the coming $6$ months. A $6-$month $42-$strike European call

option on the stock has a premium of $0\mathrm{.}36.$ The continuously compounded risk$-$free interest rate

is $5\%.$ Consider a $6-$month $42-$strike American put option on the stock. Would it be possible that

exercising the American put option now is optimal? Show all calculation and explanation.