This is NOT a real coin. It's a reproduction that has no numismatic collectible value.
It's value is just what someone will pay for it.
$20
assuming you are referring to the $20 coin, it was called a Saint Gaudens
The rarest coin is the 1933 saint gaudens double eagle. It was sold at a auction for more than 7 million!
No Saint-Gaudens $20 gold coins have been struck since 1933. The modern American Eagle Bullion coins that use a modified rendition of Saint-Gaudens design are only struck in $5, $10, $25 and $50 denominations.
Only 4 denominations were struck in 1933, the Lincoln cent a Walking Liberty Half dollar a Indian Head $10.00 gold eagle and the $20.00 Saint-Gaudens double eagle
The simple answer is: The only real one that's legal to own sold for $7,590,020.00 in July in 2002
The courts have held that the coins are illegal to own so it's very difficult to place a retail value on them. When they were privately held it was speculated they could sell for five to ten million dollars. See the related link for a full article on this famous rarity.
The A is part of the designers monogram, Augustus Saint-Gaudens. But it don't matter, the coin is a replica (fake) and has no collectible value. The 1933 Double Eagle is likely the most reproduced coin in US history, the only legal example sold in July-02 for $7,590,020
The 1933 Gold Double Eagle coin, designed by Augustus Saint-Gaudens, sold for $7.5 million in 2002, the highest price in the world ever paid for a coin.
The Saint-Gaudens Double Eagle (1907-1933) was struck at the mints in Philadelphia (no mintmark), Denver (D), and San Francisco (S). The $5, $10, $20, and $50 US bullion coins (1986-2007) using Saint-Gaudens' obverse design have been struck in Philadelphia and West Point. For several years both "circulation strikes" and proof coins were minted in Philadelphia but only the proof versions had a mintmark (P). Then for a few years, the proofs were minted in West Point (W) and none of those minted in Philadelphia were mintmarked. A couple of years ago (2004?) production of all bullion coins was moved to West Point, but I am not sure if the non-proofs carry the mintmark or not.
There is no doubt that the 1933 Saint-Gaudens Double Eagle is the most valuable US coin. One of these coins recently sold at auction for over 7 million dollars.
This depends as to what you classify as rare. Currently the most expensive coin ever sold is the 1933 golden saint gaudens eagle worth over 20 million dollars.