For this one, I didn't want to have to handstitch and I wanted my design centered, so I changed the sewing a bit.

Finished product:



First, fold your placemat so the side seams overlap 1/4" in the center.



Sew down this seam. You will have to do it in steps since the opening isn't wide enough for your sewing machine arm. The steps I did were:
starting at the top going as far as I could manage



Then starting at 2/3 way down going back towards the seam I just ended:



I had to pull the purse inside out for that seam.



Then turn the bag around and start at the middle seam and sew towards the end.



Then iron (because it will be a wrinkled mess) and fold the bottom and top to make the purse.



I added magnetic snap closures next. You can do any closure you want though (or no closure).



I wanted a chinese coin embellishment on the front, so I added that next.



Next, you add the straps. I used cording. To keep from fraying, I taped where I was going to cut an then snipped in the middle of the tape.



I then pinned it so it would lay between the layers.



I pinned it to the inside pocket so the stitching would not show on the outside of the purse.



Next I zig zagged the strap in, to make sure it was extra secure.



Then stitch up both side seams, going back and forth over the strap a few times.





That is it! Your 20 minute purse is done.