You own a lot in Key West, Florida, that is currently unused. The going

price for similar lots is currently $$1\mathrm{.}2$ million. Over the past five years,

the price of land in the area has increased $10$ percent per year, with an

annual standard deviation of $19$ percent. A buyer has recently approached you

and wants an option to buy the land in the next $9$ months for $$1,310,000.$ The

risk$-$free rate of interest is $7$ percent per year, compounded continuously.

How much should you charge for the option? Round off your answer to the

nearest $000$ dollars and show detailed calculations for each computational

step.