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$13 in good condition
You have a Liberty Seated Half Dime - a 1869-S coin in good condition (G4) is worth: $20.00; if its mint state is MS60, the value increases to: $400.
A 1857 nickel is also called: a Seated Liberty half dime. Its value in good condition (G-4) is: $20; if the mint state is MS-60, the value increases to: $250.
Please check your coin again and post a new, separate question. No half dimes were minted at San Francisco until 1863.
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This could be worth a lot of money depending on the mint and the shape of the coin. Take it to to your local coin dealer to get it appraised.
There are only 4 known genuine 1861 C.S.A. Seated Liberty half dollars. Many replicas and counterfeits exist.
The initial 5 cent coins minted by the US mint were the Shield 5 cent coins - and they were initially minted in the year 1866. Prior to that, the Draped Bust Half Dime, Capped Bust Half Dime, and the Seated Liberty Half Dime were minted. However, there were NO 5 cent coins minted in the year of 1815.
There is no such thing as a "Liberty" coin. Almost all US coins have either a depiction of Liberty or the word Liberty on them. Is this a Walking Liberty Half-Dollar? A Barber Dime? A Morgan Dollar? An Indian-Head Cent? A Seated Liberty half-dime? A gold half-eagle? A Silver Eagle? Etc. Without knowing the denomination, it is impossible to answer your question.
The 1847 Seated Liberty Half Dime was only produced in Philadelphia. It is also the type where drapery was added to the liberty on the obverse of the coin. According to USA Coin Book, the value of the coin in good condition is about $15 up to about $260 in MS60 mint condition. In MS63 choice uncirculated grade, this coin is worth about $485.
Because the value of it is worth half the value of a dime.
$30-$50 depending on condition. http://www.pcgs.com/prices/PriceGuideDetail.aspx?MS=1&PR=1&c=121&title=Liberty+Seated+Half+Dollar