To calculate Emilio's account balance at the end of the week, we need to start with his initial balance and then account for the checks he wrote and the deposit he made.
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Start with the initial balance: \[ 728.32 \]
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Subtract the amounts of the checks written:
- Check 1: $99.48
- Check 2: $33.50
- Check 3: $18.23
- Check 4: $72.05
Let's total the checks: \[ 99.48 + 33.50 + 18.23 + 72.05 = 223.26 \]
Now subtract the total of the checks from the initial balance: \[ 728.32 - 223.26 = 505.06 \]
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Now add the amount of the paycheck deposit: \[ 505.06 + 1,109.90 = 1,614.96 \]
Thus, Emilio's account balance at the end of the week is: \[ \boxed{1,614.96} \]