Sumif is January also counting blank date cells

[dsrt16]

I have sumif formulas calculating the net for the month; all of them work except January. January also counts cells that don't have a date at all. The users want to calculate their net before taxes, so the taxes date is left blank so they don't factor into any month.

However, January then returns a net applying all taxes in Quarter 1 (January, February, and March) because it is counting any cells without a date as January.

Here is the formula:
{=SUM(IF(MONTH(A10:A85)=1, E10:E85,0))}

I need it to only sum the amount if there is a January date in A10:A85, but as mentioned it is also calculating in amounts that are not given a date.

I tried

{=SUM(IF(AND(MONTH(A10:A85)=1, A10:A85<>""),E10:E85,0))}

But that just returned $0.00

 

[Dave Patton]

=sumproduct(--(month(a10:a85)=1),--(a10:a85<>0),(e10:e85))

Array enter
=SUM(IF(MONTH(A10:A85)=1,IF(A10:A85<>"",E10:E85)))

 

[dsrt16]

I solved it. I forgot I couldn't use AND in that situation.

This formula worked:

{=SUM(IF((MONTH(A11:A86)=1)*(A11:A86<>""), E11:E86,0))}