Postgres 10

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CREATE TABLE T ("day" int, "growth_rate" numeric, "target" int);
    
INSERT INTO T
    ("day", "growth_rate", "target")
VALUES
    (1, 1.2, null),
    (2, 1.3, null),
    (3, 1.4, null),
    (4, 1.2, null),
    (5, 1.1, 1000);
5 rows affected

with data as (
    select *,
        max(target) over () / exp(sum(ln(growth_rate))
            over (order by day desc)) as tgt
    from
        (select day, growth_rate, target from T union all select 0, null, null) t2
)
select day, growth_rate, coalesce(lag(tgt) over (order by day desc), target) as target
from data
order by day


day
growth_rate
target


0
null
346.87534687534688738

1
1.2
416.25041625041625388

2
1.3
541.12554112554115482

3
1.4
757.57575757575759298

4
1.2
909.09090909090909091

5
1.1
1000


with data as (
    select day,
        max(target) over () as target,
        lead(growth_rate) over (order by day) as growth_rate
    from
        (select day, growth_rate, target from T union all select 0, null, null) t2
)
select day, growth_rate,
     coalesce(target / exp(sum(ln(growth_rate))
         over (order by day desc)), target) as tgt
from data
order by day


day
growth_rate
tgt


0
1.2
346.87534687534688738

1
1.3
416.25041625041625388

2
1.4
541.12554112554115482

3
1.2
757.57575757575759298

4
1.1
909.09090909090909091

5
null
1000

day	growth_rate	target
0	null	346.87534687534688738
1	1.2	416.25041625041625388
2	1.3	541.12554112554115482
3	1.4	757.57575757575759298
4	1.2	909.09090909090909091
5	1.1	1000