Here are a few reasons why a 1977 one dollar bill with a faded yellow backside might have increased value:
1. Rarer Variant: The faded yellow color on the backside of the bill could be a result of a printing or manufacturing error, which can make it a rare variant. Such errors can attract the attention of numismatists (currency collectors) who specialize in collecting error notes.
2. Historical Interest: The 1970s were a significant period for the United States currency system. In 1976, the United States government started issuing paper currency without the "In God We Trust" motto, which was later reinstated in 1979. As such, any one dollar bill from the 1977 series can have historical significance, especially if it displays interesting variations or errors.
3. Unique Characteristics: The faded yellow backside of the bill gives it a unique appearance, which might make it more desirable for collectors interested in visually appealing currency notes.
However, it's important to note that the value of currency notes can be subjective and can vary widely depending on market demand and the specific circumstances surrounding the note. Consulting with a reputable numismatist or visiting online platforms where collectors buy and sell banknotes can help determine the potential value of your bill more accurately.