I've been reading about options and I feel as though I am missing something obvious. Let me use an example...

Stock XYZ is trading at 12.5. I see a Strike of 10 and a Price of 3. I think the stock will go up. So I purchase one option (Buy to Open?). So I've spent $300 correct? (assume no commissions)

Lets say the stock goes up to 14 with a week before expiration and I want to cash out. Would I then Sell to Close? And if so would I then have made (14-10)*100 - 300 = $100?