Most people consider used encyclopedia sets to be quite useless. Many give old sets away on Freecycle or Craig's List. Hobbyists may use them to hide valuables in. Some restaurants or bars use them as decorations on their shelves. But most use the internet for more up-to-date information. Most libraries use online encyclopedias now.
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This is going to be hard to hear and you're not going to like it:
It's worth nothing.
The value of an encyclopedia is that it presents you with facts about the world. An old encyclopedia presents you with facts about the world as it existed/was understood when it was published. Hopefully you can see why fewer people are interested in the latter.
Some of it's still true, of course. The problem is that unless you're already an expert in the field (and if you are, why are you bothering to look it up?) you can't really know what's true and what scientists today are pointing at and laughing about.
There could, I suppose, be some sentimental value in having a set from the year you were born (or graduated, or got married, or some other event). But it's not going to be much; $20 is probably way too optimistic a price.
A lot of times people will donate encyclopedias to libraries (under the mistaken impression that a library has a use for information half a century out of date). The library then turns around and sells these in library sales, usually for a few bucks for the set.
(The same is true of those 1980s National Geographic magazines you've been holding on to, by the way.)
The value of a set of Encyclopedia Americana can vary depending on factors such as the edition, condition, completeness, and demand from collectors. Older or rare editions may hold more value, while newer editions may not be as sought after. It's best to research recent sales of similar sets to get an idea of the current market value.