Problem:

Column A is a list of several different payments that are due each month. Column B indicates the date that each payment is no longer required.
We want to calculate the total amounts that need to be paid during each year listed in column C.
Solution:

Use the SUM, YEAR, and MONTH functions in the following Array formula:
{=SUM((YEAR($B$2:$B$6)>C2)*12*$A$2:$A$6+(YEAR($B$2:$B$6)=C2)*MONTH($B$2:$B$6)*$A$2:$A$6)}