Let A3:F4 house the sample you posted.
G2:H4 house specs and the result:
<TABLE style="WIDTH: 113pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0 cellPadding=0 width=151><COLGROUP><COL style="WIDTH: 58pt; mso-width-source: userset; mso-width-alt: 2730" width=77><COL style="WIDTH: 55pt; mso-width-source: userset; mso-width-alt: 2616" width=74><TBODY><TR style="HEIGHT: 14.4pt" height=19><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; WIDTH: 58pt; HEIGHT: 14.4pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" id=td_post_2628516 class=xl67 height=19 width=77>
Start date</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; WIDTH: 55pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl65 width=74 align=right>
6/1/2011</TD></TR><TR style="HEIGHT: 14.4pt" height=19><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 14.4pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl67 height=19>
End date</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl65 align=right>
3/1/2015</TD></TR><TR style="HEIGHT: 14.4pt" height=19><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 14.4pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl67 height=19>
Result</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl66 align=right>
41,140.02</TD></TR></TBODY></TABLE>
H4, control+shift+enter, not just enter:
Code:
=SUM(IF($A$3:$F$3>=YEAR(H2),IF($A$3:$F$3<=YEAR(H3),A4:F4)))-
(12-MONTH(H2))*(INDEX(A4:F4,MATCH(YEAR(H2),A3:F3,0))/12)-
(12-MONTH(H3))*(INDEX(A4:F4,MATCH(YEAR(H3),A3:F3,0))/12)