SQLite: Running balance with an ending balance - sqlite

Question

I have an ending balance of $5000. I need to create a running balance, but adjust the first row to show the ending balance then sum the rest, so it will look like a bank statement. Here is what I have for the running balance but how can I adjust row 1 to not show a sum of the first row, but the ending balance instead.
with BalBefore as (
select *
from transactions
where ACCT_NAME = 'Real Solutions'
ORDER BY DATE DESC
)
select
DATE,
amount,
'$' || printf("%.2f", sum(AMOUNT) over (order by ROW_ID)) as Balance
from BalBefore;
This gives me"
DATE AMOUNT BALANCE
9/6/2019 -31.00 $-31.00 <- I need this balance to be replaced with $5000 and have the rest
9/4/2019 15.00 $-16.00 sum as normal.
9/4/2019 15.00 $-1.00
9/3/2019 -16.00 $-17.00
I have read many other questions, but I couldn't find one that I could understand so I thought I would post a simpler question.

Answer 1

The following is not short and sweet, but using the WITH statement and CTEs, I hope that the logic is apparent. Multiple CTEs are defined which refer to each other to make the overall query more readable. Altogether the goal was just to add a beginning balance record that could be :
/*
DROP TABLE IF EXISTS data;
CREATE temp TABLE data (
id INTEGER NOT NULL PRIMARY KEY AUTOINCREMENT,
date DATETIME NOT NULL,
amount NUMERIC NOT NULL
);
INSERT INTO data
(date, amount)
VALUES
('2019-09-03', -16.00),
('2019-09-04', 15.00),
('2019-09-04', 15.00),
('2019-09-06', -31.00)
;
*/
WITH
initial_filter AS (
SELECT id, date, amount
FROM data
--WHERE ACCT_NAME = 'Real Solutions'
),
prepared AS (
SELECT *
FROM initial_filter
UNION ALL
SELECT
9223372036854775807 as id, --largest signed integer
(SELECT MAX(date) FROM initial_filter) AS FinalDate,
-(5000.00) --ending balance (negated for summing algorithm)
),
running AS (
SELECT
id,
date,
amount,
SUM(-amount) OVER
(ORDER BY date DESC, id DESC
RANGE UNBOUNDED PRECEDING
EXCLUDE CURRENT ROW) AS balance
FROM prepared
ORDER BY date DESC, id DESC
)
SELECT *
FROM running
WHERE id != 9223372036854775807
ORDER BY date DESC, id DESC;
This produces the following
id date amount balance
4 2019-09-06 -31.00 5000
3 2019-09-04 15.00 5031
2 2019-09-04 15.00 5016
1 2019-09-03 -16.00 5001
UPDATE: The first query was not producing the correct balances. The beginning balance row and the windowing function (i.e. OVER clause) were updated to accurately sum over the correct amounts.
Note: The balance on each row is determined completely from the previous rows, not from the current row's amount, because this works backward from an ending balance, not forward from the previous row balance.