These bank notes come under the heading of “trade goods”, because they actually have some value in the market, even though they do not have any value in financial institutions.
The one who owns these bank notes should work out their value at the end of the zakaah year, and pay zakaah on them at a rate of 2.5%. This applies if their value reaches the nisaab (minimum threshold) or if he has other cash which completes the nisaab.
The nisaab is the equivalent of 595 grams of silver. See the answer to question no. 2795.
And Allaah knows best.