SQL Server 2019

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create table t (Name varchar, Total int,  Payment int,   BalanceForward int,     Date date)

insert into t values
('A', NULL , NULL ,  0      , null),
('A', 20   , 40   ,  NULL   ,'01/01/2021'),
('A', 100  , 50   ,  NULL   ,'02/01/2021'),
('A', 50   , 80   ,  NULL   ,'03/01/2021'),
('B', NULL , NULL ,  30     , null),
('B', 50   , 50   ,  NULL   ,'01/01/2021'),
('B', 50   , 80   ,  NULL   ,'02/01/2021'),
('B', 50   , 40   ,  NULL   ,'03/01/2021'),
('C', NULL , NULL ,  100    , null)
9 rows affected

select * from t


Name
Total
Payment
BalanceForward
Date


A
null
null
0
null

A
20
40
null
2021-01-01

A
100
50
null
2021-02-01

A
50
80
null
2021-03-01

B
null
null
30
null

B
50
50
null
2021-01-01

B
50
80
null
2021-02-01

B
50
40
null
2021-03-01

C
null
null
100
null


with bf as (
	select * , Sum(total-payment) over(partition by name order by date) + sum(balanceforward) over(partition by name order by date) newbf
	from t
)
update bf set balanceforward=newbf
where balanceforward is null
Warning: Null value is eliminated by an aggregate or other SET operation.
6 rows affected

select * from t


Name
Total
Payment
BalanceForward
Date


A
null
null
0
null

A
20
40
-20
2021-01-01

A
100
50
30
2021-02-01

A
50
80
0
2021-03-01

B
null
null
30
null

B
50
50
30
2021-01-01

B
50
80
0
2021-02-01

B
50
40
10
2021-03-01

C
null
null
100
null

Name	Total	Payment	BalanceForward	Date
A	null	null	0	null
A	20	40	null	2021-01-01
A	100	50	null	2021-02-01
A	50	80	null	2021-03-01
B	null	null	30	null
B	50	50	null	2021-01-01
B	50	80	null	2021-02-01
B	50	40	null	2021-03-01
C	null	null	100	null