How much is White Rotary 77-122487 made by White Sewing Machine Corporation worth?

The price of your White Sewing Machine Corporation's White Rotary 77 Series machine depends a lot on it's condition. If you check e-bay it may give you a start as to the going rate for those sewing machines.

However, you may want to try to find a sewing machine store in your area or call around to the local antique shops and ask if they know about 'antique' sewing machines or if they know of someone/someplace that specializes in them, like a collector/appraiser, so that you can get a proper appraisal/value for your machine. You may even want to try any of the more prominent auction houses in your area as they generally have people on hand that specialize in different types of antiques/collectables.