Indexing for query containing xml column
If you are updating the xml that often, then consider property promotion, ie converting the xml to relational tables, as also suggested by others.

Re the design, are you storing Balance and Transaction in more than one place?  This sounds dangerous.  If the xml is a kind of history table then it might be better as that.  You could also make sure the history table is populated at the same time as the main table within a transaction so it's safe.  Your current design doesn't feel safe to me.  The fact your two UPDATEs above aren't done in a transaction is a bit worrying.  Have you had mismatches between the main table and xml?

Having said all that, I did a simple test rig to try and reproduce this problem and the UPDATEs run in under a second for me on my laptop on a 1 million row table.  Can you see anything different between this rig and your queries?

USE tempdb
GO

IF OBJECT_ID('[dbo].[account]') IS NOT NULL DROP TABLE [dbo].[account]
GO
CREATE TABLE [dbo].[account](
    [ID] [int] NULL,
    [Type] [char](10) NULL,
    [Date] [date] NULL,
    [Balance] [decimal](15, 2) NULL,
    [TRansaction] [decimal](15, 2) NULL,
    [mybal] [decimal](15, 2) NULL,
    [dailybalance] [xml] NULL,
    [AutoIndex] [int] IDENTITY(1,1) NOT NULL,
 CONSTRAINT [PK_BalanceTable] PRIMARY KEY CLUSTERED 
(
    [AutoIndex] ASC
)WITH (PAD_INDEX  = OFF, STATISTICS_NORECOMPUTE  = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS  = ON, ALLOW_PAGE_LOCKS  = ON) ON [PRIMARY]
) ON [PRIMARY] TEXTIMAGE_ON [PRIMARY]
GO


-- Generate some dummy rows
;WITH cte AS
(
SELECT TOP 1000000
    ROW_NUMBER() OVER( ORDER BY ( SELECT NULL ) ) AS rn
FROM master.sys.columns c1
    CROSS JOIN master.sys.columns c2
    CROSS JOIN master.sys.columns c3
)
INSERT INTO dbo.account ( ID, [TYPE], [Date], Balance, [Transaction], mybal, dailybalance )
SELECT
      rn AS ID
    , CHAR( 65 + ( (rn -1) % 6 ) ) AS [TYPE]
    , DATEADD( day, (rn -1) % 90, '1 Jan 2013' ) AS [Date]
    , RAND() * 10 * ( (rn -1) % 10 ) AS [Balance]
    , RAND() * 10 * ( (rn -1) % 10 ) AS [Transaction]
    , RAND() * 10 * ( (rn -1) % 10 ) AS [mybal]

    , ( SELECT CONVERT( CHAR(10), DATEADD( month, x.y, '1 Jan 2013' ), 120 ) AS "date", x.y AS "Balance", 1 AS "Transaction" FROM ( SELECT DISTINCT TOP 12 column_id y FROM master.sys.columns ) x FOR XML PATH('Row'), ROOT('Root'), TYPE ) [dailybalance]

FROM cte
GO


-- Create data for our condition
UPDATE a
SET [Date] = '28-Feb-2013',
    dailybalance.modify('insert 
&lt;Row&gt;
  &lt;date&gt;2013-02-04&lt;/date&gt;
  &lt;Balance&gt;-1&lt;/Balance&gt;
  &lt;Transaction&gt;-1&lt;/Transaction&gt;
&lt;/Row&gt;

  as last into Root[1]
  ')
FROM dbo.account a
WHERE [ID] = 257
GO

-- Covering index for the query
-- CREATE INDEX _idx ON dbo.account ( ID, [Date] )


SELECT 'before' s, * FROM dbo.account
WHERE [ID] = 257


UPDATE account
SET [dailybalance].modify('replace value of (/Root/Row[date=''2013-02-04'']/Balance/text())[1] 
with (/Root/Row[date=''2013-02-04'']/Balance)[1] +280')   
WHERE [ID] = 257 
  AND [Date] = '28-Feb-2013'  
  AND [dailybalance].exist('/Root/Row[date=''2013-02-04'']') = 1;


UPDATE account
set [dailybalance].modify('replace value of (/Root/Row[date=''2013-02-04'']/Transaction/text())[1] 
with (/Root/Row[date=''2013-02-04'']/Transaction)[1] +280')   
where [ID] = 257 
  and [Date] = '28-Feb-2013'  
  and  [dailybalance].exist('/Root/Row[date=''2013-02-04'']') = 1;


SELECT 'after' s, * FROM dbo.account
WHERE [ID] = 257


How many rows in your account table?  If your xml is actually very large, then that might explain things.  Could there be other issues such as blocking, triggers, or is the server busy?  Looking at the query, it's unlikely full-text indexing would help you much.  XML Indexing might help, but at a significant storage penalty.  The table can end up between 2-5 its original size and you don't have that much room to play with in SQL Express 2008 R2 (10GB), so again probably not recommended.  

One other thing that might help is a covering index to support the UPDATE, eg

CREATE INDEX _idx ON dbo.account ( ID, [Date] )


Try that and see if that helps your UPDATE.  If not, try and provide the additional information requested above and I'll have another look.