A 1787 quarter dollar has no value because it does not exist. Quarters were not introduced into circulation until 1796.
The American quarter dollar was introduced in 1796 to help Americans who did not want to use a half dollar or any of the smaller forms of currency. It was a commonly used amount and became even more common after the introduction of the quarter dollar coin.
When the original quarter came out in 1796, it had a picture of Lady Liberty on the front of it. The quarter changed its appearance only slightly throughout the 19th century and had a big difference in 1932 when Lady Liberty was replaced with the head of George Washington.
Since the quarter dollar was introduced, it has had several different designs. Along with the Lady Liberty to George Washington change, the design of the quarter has undergone other changes and some quarter designs are worth more than others. Quarters have had special scenes on them to celebrate American birthdays, have had different states on them and have had national parks on them.
From 1796 until 1965, quarters were created out of silver. A United States mint act in the year of 1965 changed the specifications of the quarter and allowed it to be made out of a copper and nickel blend instead of the more expensive silver.