「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:
《玉篇》帷也,張也,幬也。
「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:
按:此字本為帳幕之義,後亦用為錢項計簿之義,此義或从貝作「賬」。清.翟灝《通俗編.貨財》云:「幃幄曰帳,而計簿亦曰帳者,運籌必在幃幄中也。今市井或造賬字用之,諸字書中皆未見。」
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.