You own a lot in Key West, Florida, that is currently unused. Similar lots have recently

sold for $$1,380,000.$ Over the past five years, the price of land in the area has increased

$4$ percent per year, with an annual standard deviation of $27$ percent. A buyer has

recently approached you and wants an option to buy the land in the next $12$ months for

$$1,530,000.$ The risk$-$free rate of interest is $4$ percent per year, compounded

continuously. How much should you charge for the option? $($Do not round intermediate

calculations and enter your answer in dollars, not millions, rounded to $2$ decimal

places, e$.$g$.,1,234,567\mathrm{.}89.$

Answer is complete but not entirely correct.