With the dates in D2 and down and the original data in columns A:C and the account in E2 the dates in column F enter this is G2 and fill down to give the count each day for the account named.
Formula:
=SUMPRODUCT( ($A$2:$A$100=$E$2)*(LEFT($B$2:$B$100,5)=LEFT(F2,5)))
This treats each date and time as a serial number and uses only the left 5 digits.
If you want to use the Date function:
Formula:
=SUMPRODUCT( ($A$2:$A$100=$E$2)*(DATE(YEAR($B$2:$B$100),MONTH($B$2:$B$100),DAY($B$2:$B$100))=DATE(YEAR(F2),MONTH(F2),DAY(F2))))
To just get the transactions for each day modify the formula to
Formula:
=SUMPRODUCT( ($A$2:$A$100>0)*(DATE(YEAR($B$2:$B$100),MONTH($B$2:$B$100),DAY($B$2:$B$100))=DATE(YEAR(F4),MONTH(F4),DAY(F4))))
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