Assigning payment values to consecutive months

Transact-SQL
1

I have a table where I am looking at authorizations and their monthly value. I have taken the total value of the auth for the number of months and divided it by the number of months the auth is valid to give me a monthly amount. To aggregate the data, I need to somehow assign the monthly value to each month during that auth time frame. For example, I have an auth that started on 8/1/2017 and ends on 1/31/2018 which is 6 months in duration. The total value of the auth is $3559.50 so per month it is $593.25 so I need to somehow in my aggregate assign $593.25 to each month from August to January. I'm looking for this in results.
Month member amount
8/1/2017 12345 593.25
9/1/2017 12345 593.25
10/1/2017 12345 593.25
11/1/2017 12345 593.25
12/1/2017 12345 593.25
1/1/2018 12345 593.25

Here is sample data:
create table #temp
(month date,
memberId varchar(5),
auth_datefrom date,
auth_dateto date,
authmonths int,
est_monthly_payment money)

INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','12345','8/1/2017','9/30/2017','2','762.75');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','67890','8/1/2017','9/30/2017','2','2440.8');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','23456','8/1/2017','6/30/2018','11','443.78');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','34567','8/1/2017','8/31/2017','1','1708.56');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','45678','8/1/2017','8/31/2017','1','4881.6');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','56789','8/1/2017','11/1/2017','3','996.66');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','67890','8/1/2017','6/30/2018','11','443.78');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','78901','8/1/2017','8/31/2017','1','1708.56');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','89012','8/1/2017','8/31/2017','1','4881.6');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','90123','8/1/2017','2/28/2018','7','813.6');
INSERT INTO #temp (Month,member_id,auth_datefrom,auth_dateto,authmonths,Est_Monthly_Payment) VALUES ('8/1/2017','1234','8/1/2017','6/30/2018','11','443.78');

2

so would the following
2017-08-01 2017-09-30 2 762.75

result in 2 months ?
08-01 381.37
09-01 381.37

3

The 762.75 is per month so 8/1 would be 762.75 and 9/1 would be 762.75.

4

I received this from another user but I can't figure out how to adjust the counter date to be the auth_datefrom instead of the 8/1/2017. When I add the from #temp in the initial select statement, it calculates the months for the first row and assigns the same values to all rows. So I guess if I need to inidcate the auth dates for a particular auth, I need some way of referencing it because each auth has different start dates. Does anyone know how I can change the start date of the counter from 8/1/2017 to the dynamic auth_datefrom?

CREATE TABLE #DateTable (Dates DATETIME, ID INT IDENTITY )

DECLARE @Counter INT
SET @Counter = 0

WHILE @Counter < 481

BEGIN 
INSERT INTO #DateTable
SELECT DATEADD (MONTH, @Counter, '2017-08-01') 
SET @Counter = @Counter + 1

END

SELECT D.*, T.member_Id, T.auth_datefrom, T.auth_dateto, T.authmonths, 
T.est_monthly_payment 
FROM #DateTable AS D
CROSS JOIN  #temp AS T 
WHERE D.ID <= T.authmonths