Let's first calculate Elsbeth’s account balance step by step, starting from Monday.
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Initial balance on Monday: \[ -16.75 \]
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On Tuesday, Elsbeth deposited $5.72: \[ -16.75 + 5.72 = -11.03 \]
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On Thursday, she deposited $16.75: \[ -11.03 + 16.75 = 5.72 \]
Now her balance is $5.72 before the Friday deposit.
- On Friday, Elsbeth deposited her paycheck of $872.56: \[ 5.72 + 872.56 = 878.28 \]
Thus, the account's final total balance on Friday is: \[ \text{$878.28} \]
Therefore, the answer is: $878.28.