Q:

How to keep a running balance of payments vs. billings in Excel

I have a row of cells with 12 Monthly columns, G4 (January) through R4 (December), in which I will input the amount paid towards a monthly billing. [Note that an early comment discusses multiple years in multiple rows.  However, that is no longer the case; it is just a single year, in row 4.]
When the bill has an amount due, it is a standard amount, the value of which is stored in cell F4. 
If a month does not have an amount due, I leave the associated G4:R4 cell blank.  If an amount is due, I enter the amount paid (zero if nothing), in the associated cell.  
I would like for cell A4 to show a running total of the outstanding balance (amounts due minus amounts paid).  Example: Monthly bill is 100.00 (F4). I paid 75 dollars in January (G4), so the running total I still owe is 25.00 (A4). I paid 50 dollars in February towards February's bill (H4), so now I owe 75 (A4).  
Note that there will never be a case where there is no billed amount but I pay toward a prior balance; if there is a prior balance, there will always be a billing for the standard amount.  So, a blank cell in G4:R4 means that nothing was billed; a value in G4:R4 means the standard amount was billed and the entered amount was paid.   

A:

In A4 simply put:
=$F4*COUNT($G4:$R4)-SUM($G4:$R4)

EDIT:
 after your comment removed some "$" signs so that the formula can be easily copied over the 15 needed rows.

