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.
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.
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.