array formula: sum to date

Question

I have a number of invoices:

invoice #	start	end	paid on	amount	paid to date (hardcoded)
1	01/01/2020	30/01/2020	01/02/2020	£10.00	£10.10
2	01/02/2020	20/02/2020	01/03/2020	£7.50	£17.60
3	21/02/2020	30/02/2020	01/03/2020	£2.50	£20.10
4	01/01/2000	30/01/2000	01/03/2000	£0.10	£0.10

Where the invoices

• are not necessarily sorted by start and end date
• are not necessarily sorted by paid date.
• might not have a paid-on value.

I want to add a field called paid to date that would show me the amount I have been paid so far where it would add the amount for:

• the current invoice
• the invoices that were paid prior to this invoice's paid-on date.
• the invoices with the same paid-on date as this invoice but with a start date <= this invoice's start date.

Effectively mirroring the hard-coded column.

This is how I do it with a query (which might not be the simplest/most elegant way of doing it)

=Index(
    query(
      A1:E10, 
      "select SUM(E)
      where D is not null
      and (
        D < date '"& TEXT( D2,"yyyy-mm-dd")&"' 
        OR (
          D = date '"& TEXT( D2,"yyyy-mm-dd")&"'
          and
          B <= date '"& TEXT( B2,"yyyy-mm-dd")&"'
        )
      )"
    ),
    2, 1
  )

which is all well and good. but I want to be able to do it with array-formula, so I can have it auto-generated for me.

I tried using it inside array-formula but the value is only ever generated for the first row. I guess it's misinterpreting the range I am passing as the range of the query function, ie A1:E10. is there an easy way of fixing it?

Do I need to use VLookup?

Here is a sample spreadsheet.

Answer 1

If you have Excel 365, you can Filter directly.
Note that I am using a table with structured references. Then you don't need to adjust the range references as you add/remove rows from the table.

=SUM(FILTER([amount],([paid on]<[@[paid on]])+(([paid on]=[@[paid on]])*([start]<[@start])),0),[@amount])

This part does the filtering:

...([paid on]<[@[paid on]])+(([paid on]=[@[paid on]])*([start]<[@start]))...

Note: You can use the same algorithm in Sheets:
Note that I am using regular addressing, and also using a semicolon instead of a comma for the argument separators

=sum(iferror(FILTER($E$2:$E$5;($D$2:$D$5<$D2)+(($D$2:$D$5=$D2)*($B$2:$B$5<$B2)));0);E2)

Answer 2

try:

=INDEX(IFNA(VLOOKUP(A2:A, {INDEX(SORT({A2:B, D2:E}, 2, 1, 3, 1),,1), 
 MMULT(TRANSPOSE((ROW(E2:E)<=TRANSPOSE(ROW(E2:E)))*
 INDEX(SORT({A2:B, D2:E}, 2, 1, 3, 1),,4)), SIGN(E2:E))}, 2, 0)))