Calculating compound interest with deposits/withdraws - sql

Question

I'm trying to calculate the total on an interest-bearing account accounting for deposits/withdraws with BigQuery.
Example scenario:
Daily interest rate = 10%
Value added/removed on every day: [100, 0, 29, 0, -100] (negative means amount removed)
The totals for each day are:
Day 1: 0*1.1 + 100 = 100
Day 2: 100*1.1 + 0 = 110
Day 3: 110*1.1 + 29 = 150
Day 4: 150*1.1 + 0 = 165
Day 5: 165*1.1 - 100 = 81.5
This would be trivial to implement in a language like Python
daily_changes = [100, 0, 29, 0, -100]
interest_rate = 0.1
result = []
for day, change in enumerate(daily_changes):
if day == 0:
result.append(change)
else:
result.append(result[day-1]*(1+interest_rate) + change)
print(result)
# Result: [100, 110.00000000000001, 150.00000000000003, 165.00000000000006, 81.50000000000009]
My difficulty lies in calculating values for row N when they depend on row N-1 (the usual SUM(...) OVER (ORDER BY...) solution does not suffice here).
Here's a CTE to test with the mock data in this example.
with raw_data as (
select 1 as day, numeric '100' as change union all
select 2 as day, numeric '0' as change union all
select 3 as day, numeric '29' as change union all
select 4 as day, numeric '0' as change union all
select 5 as day, numeric '-100' as change
)
select * from raw_data

Answer 1

You may try below:
SELECT day,
ROUND((SELECT SUM(c * POW(1.1, day - o - 1))
FROM t.changes c WITH OFFSET o), 2) AS totals
FROM (
SELECT *, ARRAY_AGG(change) OVER (ORDER BY day) changes
FROM raw_data
) t;
+-----+--------+
| day | totals |
+-----+--------+
| 1 | 100.0 |
| 2 | 110.0 |
| 3 | 150.0 |
| 4 | 165.0 |
| 5 | 81.5 |
+-----+--------+

Answer 2

Another option with use of recursive CTE
with recursive raw_data as (
select 1 as day, numeric '100' as change union all
select 2 as day, numeric '0' as change union all
select 3 as day, numeric '29' as change union all
select 4 as day, numeric '0' as change union all
select 5 as day, numeric '-100' as change
), iterations as (
select *, change as total
from raw_data where day = 1
union all
select r.day, r.change, 1.1 * i.total + r.change
from iterations i join raw_data r
on r.day = i.day + 1
)
select *
from iterations
with output