Sumif between date ranges depending on condition

Good afternoon everyone !

Here's the situation.

The first sheet, SHEET A. I have a name column, and many date range columns going from 01/01/2015-01/31/2015 all the way to the present. This date range is the result of a formula I wrote. The names signify employees, and in the spaces under the date ranges, I want to put the total amount that employee spent in that time period, if they spent any.

Name | 01/01/2015-01/31/2015 | 02/01/2015-02/28/2015 | ....
Jeff
Bob

The data regarding spending comes from another sheet with three columns, which I will call SHEET B

Name | Date | Amount Spent
Jeff 01/15/2015 $15
Jeff 01/24/2015 $30
Bob 01/03/2015 $55
Bob 02/04/2015 $10

...and so on and so forth.

What I'm looking for is a formula which will calculate the total amount an employee spent in SHEET B in a given month and enter it into the appropriate cell in SHEET A based on the date ranges in the first row.

I have attached a sample worksheet if the above is not a good description. Is this possible? Thanks.

For transperancy sake here is the formula for the date ranges : =TEXT(DATE(2015,COLUMN(A:A),1),"MM/DD/YY")&"-"&TEXT(DATE(2015,COLUMN(A:A)+1,1)-1,"MM/DD/YY")