Thank you for submitting your item for appraisal. As you already correctly stated, this is a persian Nain rug of good quality. A oriental rug classic so to speak. Nain rugs are a common sight at auctions. Very similar rugs in size and colour can be bought for a few hundred dollars if in slightly used conditon.
The rug in your possession is in perfect condition, therefore the estimate is higher. "Asking prices" in the trade are often much higher.