=SUMPRODUCT( (MONTH($A$2:$A$6)=1) * ($B$2:$B$6) )
Explanation:
(MONTH($A$2:$A$6)=1)
creates an array of 1 and 0, it's 1 when the
month is january, thus in your example the returned array would be [1, 1, 1, 0, 0]
SUMPRODUCT
first multiplies each value of the array created in the above step with values of the array ($B$2:$B$6)
, then it sums them. Hence in
your example it does this: (1 * 430) + (1 * 96) + (1 * 440) + (0 * 72.10) + (0 * 72.30)
This works also in OpenOffice and Google Spreadsheets