The 1962 quarter was one of the last US silver quarter series minted. Many of these coins were minted so they don't have much numismatic value. But the 90% silver content gives the coins bullion value regardless of condition.
Type: Washington Quarter
Face Value: $0.25
Composition: 90% silver, 10% copper
Silver Weight: 5.62 grams
Total Weight: 6.25 grams
Current Silver Bullion Value: $3.22
The US minted the 1962 quarter with no mint mark and also the 1962 D quarter. The mint mark can be found on the reverse side of the coin.
The value in circulated condition is worth at least its weight in silver. The scrap silver value for this coin is $3.22 as of September 19, 2019. This scrap value is calculated from the current silver spot price of $17.83 per ounce.
Both the 1962 quarters with no mint mark and the 1962 D quarters are common. But in uncirculated condition each coin will sell for a premium. The Philadelphia quarters with no mint mark each sell for around $8 in uncirculated condition, while the D quarters each sell for about a $3 premium above the scrap silver price.
Proof coins are available and they are valued at around $10 each. Graded proof coins with a grade of PR 67+ will sell for more. Over three million collectible proof coins were issued so they aren't rare.