Beer stopped fermenting

You are probably done fermenting. And it sounds like everything went well. Don't do anything to raise the FG. Depending on what your measured OG was, it sounds like your yeast performed above the average range of attenuation. This is good in this case as most people would probably rather have their IPA finish at 1.013 instead of 1.018.

If this were my beer, I would let it sit another 10 days and then package.

Sidenote: If you hit 1.062 OG, then your beer is 6.4% ABV and your apparent attenuation is 78%, just on the high side of average for a yeast like 1056 (assuming that's what you used).

 

If the recipe mentioned those two gravities, what that means is the OG (after brewing and before pitching) is supposed to be 1.062 and the FG (after fermentation is complete) should be 1.018. If your FG is 1.013, that's a good thing as stated above.

 

Either you wrote this wrong (or I'm reading it wrong) or there is some misconception. But about fermentation; your yeast were still active (fermenting) long after the two days . . . I suspect you are relying on airlock activity for your observation. Here is an excellent article on what's going on in your fermentor. It's a long read, but if you take the time to read the entire chapter on Fermentation you should gain good insight on what's going on. From your description, everything appears to be normal . . . if my Citra IPA finished at 1.013 I would be pleased. Don't be in a hurry to bottle, I use 2 weeks as minimum time in primary (see link above).

 

I agree with all of the assessments above that your beer is okay, and that fermentation is essentially complete. Since you are using a carboy then you probably observed the krausening that occurred and subsided during those first few days. That's the surest sign that fermentation did occur. The gravity readings that you take now will only confirm that it is finished, and if you have two identical readings that are taken a few days apart, then that confirms that no more sugar is being fermented into alcohol, thus the beer is done. A short conditioning period after fermentation is always a recommended thing to do, so wait a few days before you package the beer.

 

1.013 at room temperature?
If so, the FG could be closer to 1.015.