The U.S. never minted a silver penny. For starters, it would be worth more than a dime! Your coin was plated for use in jewelry or something similar. That makes it an altered coin worth face value only.
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It's called a Kennedy half and it's not silver. All circulating halves dated 1971 and later are made of copper and nickel. It's only worth 50¢.
ALL U.S. coins have the word Liberty on them. The term "Liberty" coin is reserved for those like old dimes and quarters that actually have the image of Miss Liberty.
The 1936 Walking Liberty US Half Dollar can be valued between $14.00 to $265 depending on the condition of the coin from G-4 to MS-65. The average sale price online usually falls between $12.00 -$20 There were 12,617,901 minted so it is not a particularly rare coin but rather one of the more common Walking Liberty Half Dollars
The coin is actually a "Statue of Liberty Centennial" half dollar. None were struck in silver it is a clad coin. It was issued as Proof and Uncirculated and both are very common with the same average retail value of $5.00.
It is not a Liberty half dollar, it is a Kennedy half dollar. Unless in a mint set they are worth 50 cents. They are in common circulation.