Running assignment of values with break T-SQL

With the below table of data

Customer	Amount Billed	Amount Paid	Date
1	100	60	01/01/2000
1	100	40	01/02/2000
2	200	150	01/01/2000
2	200	30	01/02/2000
2	200	10	01/03/2000
2	200	15	01/04/2000

I would like to create the next two columns

Customer	Amount Billed	Amount Paid	Assigned	Remainder	Date
1	100	60	60	40	01/01/2000
1	100	40	40	0	01/02/2000
2	200	150	150	50	01/01/2000
2	200	30	30	20	01/02/2000
2	200	10	10	10	01/03/2000
2	200	15	10	-5	01/04/2000

The amount paid on each line should be removed from the amount billed and pushed onto the next line for the same customer. The process should continue until there are no more records or the remainder is < 0.

Is there a way of doing this without a cursor? Maybe a recursive CTE?

Thanks

Answer

As I mentioned in the comments, this is just a cumulative SUM:

WITH YourTable AS(
    SELECT *
    FROM (VALUES(1,100,60 ,CONVERT(date,'01/01/2000')),
                (1,100,40 ,CONVERT(date,'01/02/2000')),
                (2,200,150,CONVERT(date,'   01/01/2000')),
                (2,200,30 ,CONVERT(date,'01/02/2000')),
                (2,200,10 ,CONVERT(date,'01/03/2000')),
                (2,200,15 ,CONVERT(date,'01/04/2000')))V(Customer,AmountBilled,AmountPaid,[Date]))
SELECT Customer,
       AmountBilled,
       AmountPaid,
       AmountBilled - SUM(AmountPaid) OVER (PARTITION BY Customer ORDER BY [Date] ASC
                                            ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) AS Remainder,
       [Date]
FROM YourTable
ORDER BY Customer,
          [Date];

Note this returns -5 for the last row, not 5, as 200 - 205 = -5. If you want 5 wrap the whole expression in an absolute function.