How to calculate running balance using PostgreSQL window functions?

Question

I want a query to track interest on a mortgage account. For simplicity assume the interest is calculated yearly. There are also one-off deposits/withdrawals (repayments etc).

I want to query this information and calculate a running balance, presumably using window functions. Here is an example of the kind of table I want to query.

year | changes | interest | comment
2020 | 10000   | 2.5      | initial mortgage of 10k
2021 | 0       | 2.0      | next year the rate drops
2022 | 5000    | 2.0      | we borrow an extra 5k
2023 | 0.      | 1.5      | rate drop again

I want a query that calculates the running balance each year, like so:

year | changes | interest | balance
2020 | 10000   | 2.5      | 10250.0 = 10000 * (1 + 2.5 / 100)
2021 | 0       | 2.0      | 10455.0 = 10250 * (1 + 2.0 / 100)
2022 | 5000    | 2.0      | 15764.1 = (10455 + 5000) * (1 + 2.0 / 100)
2023 | 0.      | 1.5      | 16000.56 = 15764.1 * (1 + 1.5 / 100)

How to do this in PostgreSQL?

Answer 1

Because of the need to multiply the prior year balance by the current interest, this is most easily achieved using a recursive CTE:

WITH RECURSIVE CTE AS (
  SELECT t.year, t.changes, t.interest, t.changes * (1.0 + t.interest / 100.0) AS balance
  FROM transactions t
  WHERE year = (SELECT MIN(year) FROM transactions)
  UNION ALL
  SELECT t.year, t.changes, t.interest, (t.changes + CTE.balance) * (1.0 + t.interest / 100.0)
  FROM transactions t
  JOIN CTE ON t.year = CTE.year + 1
)
SELECT year, changes, interest, ROUND(CAST(balance AS numeric), 2) AS balance
FROM CTE

Output:

year    changes     interest    balance
2020    10000       2.5         10250.00
2021    0           2           10455.00
2022    5000        2           15764.10
2023    0           1.5         16000.56

Demo on dbfiddle

Answer 2

The recursive CTE is quite possibly the better approach. But it is possible to do this using window functions.

The three key ideas are:

• Using exp(sum(ln())) as the product() aggregation function.
• Projecting each value to the latest time, accumulating all interest functions.
• Dividing by the "accumulated interest" up to that value to adjust for new values entering in.

The actual code is not that complicated:

select t.*,
        (sum(changes * running_interest) over (order by year) /
         coalesce(prev_running_interest, 1)
        ) as val
from (select t.*, 
             exp(sum(ln(1 + interest / 100)) over (order by year desc)) as running_interest,
             exp(sum(ln(1 + interest / 100)) over (order by year desc rows between unbounded preceding and 1 preceding)) as prev_running_interest
      from t
     ) t
order by year;

You will notice in the db<>fiddle the slight inaccuracies caused by floating point arithmetic. You can always cast to fewer decimal places for more aesthetically appealing numbers.