Here in VA you could get an appraisal for quite a bit less than $50. There are several different kinds of appraisals, too; for insurance purposes; for donating to a museum; just for information; to determine age/date/details, etc. It sounds like you are just interested in an evaluation for approx. age, right?
There are several reasons this top likely does not have much value.
Your top is incomplete.
There is no "quilting" to evaluate.
It may have been made in different periods, and by different people.
It does not have specialized or intricate piecing in the body or borders.
The workmanship may be 'okay' at best.
It may have fabrics from different periods.
You have no provenance about it.
This is not to say it isn't a quilt top worth loving and saving! But, of financial value? Probably less than you would hope.
If you are interested I can send the name/number of an AQS Certified Appraiser here in VA who could at least tell you how/where to go from here.
Jan in VA