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Washington quarters were made of 90% silver from 1932 to 1964, but 1945 is not a rare year. In lower grades the coin's value is mostly determined by the value of the silver it contains. The coin's melt value is about 0.18 times the current price of 1 oz of silver.

Look on the back of the coin to see if there's a small mint mark letter below the bow in the wreath. It may be blank or there may be a D or S.

Numismedia lists the following approximate retail values as of 01/2013:

No mint mark (Philadelphia):

Almost no wear - $9.50

Uncirculated - $10.06 to $4380.00 depending on quality

"D" mint mark (Denver):

Almost no wear - $9.90

Uncirculated - $13.80 to $468.75

"S" mint mark (San Francisco):

Almost no wear - $9.50

Uncirculated - $10.06 to $3750.00

DISCLAIMER: The retail values quoted are the best available as of the date shown, but may vary due to market fluctuations. Also the wholesale (buying) price of a coin will be less than the selling (retail) price. A reputable coin dealer will be able to give a more accurate valuation based on inspection of the coin.

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Q: What is the value of a 1945 US quarter?
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