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Did you look under the horse? It's dated 1999, the year the coin was struck. 1787 is the year Delaware became the First State.
The top date of 1787 makes it a Delaware, Pennsylvania, or New Jersey quarter, all of which were actually minted in 1999. The coin is worth 25 cents.
Uh, please look at your pocket change. ALL of the state quarters have double dates on them, one for the year the coin was minted and one for the year that the coin's state was admitted to the Union. That means you have a coin honoring Pennsylvania, Delaware, New Jersey, etc. because they were admitted in 1787.Billions of each of these have been made, so your coin is worth the same amount as all of the other state quarters out there, 25 cents.
OMG: The Denver Mint wasn't even thought of in 1787, the date 1999 is clearly struck on the same side of the coin and it's just one of the first 3 State Quarters that's only worth 25 cents.
Given that the U.S. Mint didn't begin production until 1793, odds are that your quarter features Delaware, Pennsylvania, or New Jersey, all of which became states in 1787. The coin was minted in 1999, and is worth exactly twenty-five cents.