Calculate row value based on previous and actual row values
Assuming that stmnt_date has a UNIQUE constraint, this would be fairly easy with window/analytic functions:

SELECT 
    s.stmnt_date, s.debit, s.credit,
    SUM(s.debit - s.credit) OVER (ORDER BY s.stmnt_date
                                  ROWS BETWEEN UNBOUNDED PRECEDING
                                           AND CURRENT ROW)
        AS balance
FROM
    statements AS s
ORDER BY
    stmnt_date ;


Unfortunately, MySQL does not (yet) have implemented analytic functions. You can solve the problem either with strict SQL, by self-joining the table (which should be rather inefficient although working 100%) or by using a specific  MySQL feature, variables (which would be quite efficient but you'd have to test it when upgrading mysql, to be sure that the results are still correct and not mangled by some optimization improvement):

SELECT 
    s.stmnt_date, s.debit, s.credit,
    @b := @b + s.debit - s.credit AS balance
FROM
    (SELECT @b := 0.0) AS dummy 
  CROSS JOIN
    statements AS s
ORDER BY
    stmnt_date ;


With your data, it will result in:

+------------+-------+--------+---------+
| stmnt_date | debit | credit | balance |
+------------+-------+--------+---------+
| 2014-05-15 |  3000 |      0 |    3000 |
| 2014-06-17 | 20000 |      0 |   23000 |
| 2014-07-16 |     0 |   3000 |   20000 |
| 2014-08-14 |     0 |   3000 |   17000 |
| 2015-02-01 |  3000 |      0 |   20000 |
+------------+-------+--------+---------+
5 rows in set (0.00 sec)