SQL Server 2022

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with data(name, amount, dat, discount) as (
	select 'Peter', 100, convert(DATE, '01-01-2023',105), 4  union all
	select 'Peter', 100, convert(DATE,'02-01-2023',105), 20  union all
	select 'Peter', 100, convert(DATE,'03-01-2023',105),5  union all
	select 'John', 500, convert(DATE,'01-01-2023',105),40  union all
	select 'John', 500, convert(DATE,'02-01-2023',105),3  union all
	select 'Sara', 200, convert(DATE,'01-01-2023',105),9  union all
	select 'Sara', 200, convert(DATE,'02-01-2023',105),10  -- union all
),
rdata as (
	select * from (
		select d.name, d.amount, d.dat, d.discount / 100.0 as discount, 
			log(1.0 - (d.discount / 100.0)) as ln_rest_factor, 
		row_number() over(partition by name order by dat) as rn
		from data d
	) d
)
select name, amount, discount, coalesce(lag(discount_rest) over(partition by name order by rn),amount) - discount_rest as discount_amount, discount_rest 
from (
	select name, amount, discount, round(amount * exp(sum_factor),2) as discount_rest, rn
	from (
		select name, amount, dat, discount, rn, ln_rest_factor,
			sum(ln_rest_factor) over(partition by name order by rn) as sum_factor
        from rdata
	) d
) d
order by name, rn
;

name	amount	discount	discount_amount	discount_rest
John	500	0.400000	200	300
John	500	0.030000	9	291
Peter	100	0.040000	4	96
Peter	100	0.200000	19.2	76.8
Peter	100	0.050000	3.84	72.96
Sara	200	0.090000	18	182
Sara	200	0.100000	18.2	163.8