「賬」is said to be a derivative character (分化字) of「帳」, itself being a derivative character of「張」. The meaning of「帳」is related to tents, screens, or curtains:
「賬」has meanings relating to accounts, bills, and debt, but I don't quite see the connection to「帳」. Outlier outlines the semantic extension like so:
- (orig.) to pitch a tent
- → tent, canopy
- ⇒ accounting records (written on cloth of some sort)
However, the jump from 2. and 3. seems a bit big. Is there something missing in between this gap, or a more detailed explanation describing this jump?
Also branching a bit from the above, but is the relation between「帳」and「賬」similar to that of「帖」and「貼」, in the sense that the latter is derived from the former?
Edit: From Taiwan MoE's 異體字字典:
Seems like this briefly touches on this semantic extension, but I'm hoping someone else can verify this, or provide more insight on the topic.