These are selling from $5 to $7 for the proof in the original government box with the certification. A private collector will pay more. They were over produced and are very common. They are made of copper and nickel not silver. These are the two factors that keep the value of this coin down.
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ALL American dimes have the word LIBERTY on them so that's not a distinguishing feature. Dimes dated 1946 and later are normally called Roosevelt dimes because they show a picture of President Franklin Roosevelt.
It depends on which of the 4 gold bullion coins ( $5-$10-$25-$50 ) all dated 1986 your asking about? Each denomination shows it's weight on the reverse. Multiply the weight by the spot price of gold to get the value.
If your coin has the word Liberty at the top and a picture of JFK on the front it's a Kennedy half, not a Liberty half. These are regular circulation coins and are only worth face value if you found it in change.
If it has a picture of the Statue of Liberty, it's a commemorative coin issued to mark the statue's centennial. In its original package, it sells for about $5 as of 01/2012
It depends on the condition and mintmark.
If it is an uncirculated Philadelphia, it is worth $7. An uncirculated Denver is $5.50. A proof San Francisco is $10. Otherwise, it's face value.
P.S. These are 2008 rates, so it could be worth more
The person shown on the front of a 1980 US $1 coin is womens' rights advocate Susan B. Anthony, not Miss Liberty. Please see the Related Question for details.