Yes and no.. You are certainly not overpaying and that is grreat. But what is your plan for this equity? You are just buying, you would be foolish to attempt to refi as soon as you close with the new costs again.
It is a comfort to know that you bought really fairly and you are one of the few who have a bank appraiser who just does not "comp out" the purchase at your purchase price. Most appraisers have been struggling just to verify the Purchase and Sales Agreement price.
So, congratulations.. .for now.. You know that any appraisal is a "moment in time" which can change when a new closing happens down the street from you. I anticipate they will continue to rise though, and wish you luck in your new property.