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[money paid or owed] on a debt. I paid twelve dollars on account last month. Wasn't that enough? I still have $100 due on account.
on someone's account
because of someone. Don't do it on my account. They were late on Jane's account.
on somebody's account
if you do something on someone's account, you do it because of that person Don't cook anything special on my account. I'm not even very hungry.
In part payment of a debt, as in He paid half the amount on account. [Early 1600s]
on (someone's) account
For someone's benefit: It's nice of you to make such an effort on his account.