In your first scenario, credit sales are being debited to AR and credited to Sales. If they hold Sales open past year end to get that number higher, then AR ends up being affected as well– they have to hold it open also so that things will still balance. You send the AR confirmations for the higher supposed year end number, and the customers (assuming they are paying attention to the date) give the answer of the true year end number, which is lower.
In your second scenario, as customers are paying off their accounts, the entries are DR Cash, CR AR. Holding AR open means that confirmations sent out with the figure from the supposed year end will be lower than the true AR number, and the customer (again assuming they are paying attention to the date) know they hadn't paid their bill yet and report the higher number that they owed at true year end.
Does that help?
Edited to add: You can also jot down some actual numbers if that helps you think through it:
Scenario 1
Sales is held open to make it seem higher – confirms are sent out with these figures:
AR 130,000
Sales 130,000
True figures at YE – customers confirm based on this:
AR 100,000
Sales 100,000
Scenario 2
AR is held open to make it seem like they aren't owed as much money and they have more cash – confirms are sent out based on this:
Cash 160,000
AR 120,000
True figures at YE – customers confirm based on this:
Cash 140,000
AR 140,000
(These aren't necessarily realistic numbers, but they are only meant to help simplify things. Sometimes it helps to think in terms of real numbers rather than just conceptually.)
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