Ответ для задачи на MySQL

select
  @c := if(s_charges.summ is null, 0, s_charges.summ) as charge,
  @p := if(s_payments.summ is null, 0, s_payments.summ) as payment,
  @d := if(@u = users.id, @d + @c - @p, @c - @p) as debt,
  @u := users.id as user_id,
  periods.id as period_id
from users
  left join periods on true
  left join (select sum(value) as summ, user_id, period_id from charges group by user_id, period_id) as s_charges
    on s_charges.user_id = users.id and s_charges.period_id = periods.id
  left join (select sum(value) as summ, user_id, period_id from payments group by user_id, period_id) as s_payments
    on s_payments.user_id = users.id and s_payments.period_id = periods.id
  join
    (select @c := 0, @p := 0, @d := 0, @u := 0) var
group by
  users.id, periods.id