Months Outstanding DAX Calculation - ssas

Question

I think maybe the way I'm asking this question is making it unclear. Here is another attempt:
I am trying to create a measure that counts the number of months it takes to reach an ending accounts receivable balance. As an example, I start with a measure that calculates an ending AR balance which is a calculation of values from different columns and tables and must look at every AR transaction regardless of date (that measure is already available.) What I now need to do is figure out how many months, counting backwards and including any fractional amount, starting with the most recent month (either selected or today's date) it takes to accumulate fees that add up to the ending ar balance. As an example, assuming we're looking at an AR balance at the end of 2016 $1,000:
Ending December AR Balance $1,000
December Fees: $200
November Fees: $300
October Fees: $400
September: $300
Using these values, the Months outstanding would be 3.33 (200 + 300 + 400 + (100/300).)
-- Original Question --
I'm trying to create a measure in DAX that calculates a Months Outstanding value. Essentially, the months outstanding calculation takes the final accounts receivable for an individual and counts back each month that it took to get to that value. As an example, if the final AR balance is $100 and each prior month had AR billings of $25 each month, the months outstanding would be 4 months.
I have come up with something that I believe is a start, but probably isn't even close:
Months Outstanding:=
VAR TotalBalance = [Ending Balance]
RETURN
CALCULATE(
DISTINCTCOUNT('Date'[Month]),
FILTER(
ALL('Date'[Month]),
[WIP Billings] + [AR Billings] < TotalBalance
)
)
In the above example, I'm trying to count the number of months it takes before the sum of WIP Billings and AR Billings exceeds TotalBalance (WIP and AR Billings are simply measures that are the sum of their respective columns.)
Thanks,
Eric
Edit
Here is the calculation for Ending Balance. The fact tables (Billing, Disbursement, Time, BilledDisbursement, BilledFee, MatterCredit) have references to Date, Matters, Clients, and Personnel
WIP Balance:=
ROUND(SUM(Disbursement[ToBillAmount])
+SUM('Time'[ToBillAmount])
-SUM(BilledDisbursement[ToBillAmount])
-SUM('BilledFee'[ToBillAmount])
-SUM('Matter Credit'[WIPBallance]), 2)
End WIP Balance:=
CALCULATE(
[WIP Balance],
FILTER(
ALL('Date'[Period]),
'Date'[Period] <= MAX('Date'[Period])
)
)
Ending AR Balance:=
CALCULATE(
SUM(Billing[ARAmount]),
FILTER(
ALL('Date'[Period]),
'Date'[Period] <= MAX('Date'[Period])
)
)
Ending Balance:= [Ending AR Balance] + [End WIP Balance]