Linq query sum up the amount column

Firstly, you're using SingleOrDefault which will only select a single value. You want to use Sum instead. Also, you don't need an anonymous type here. You can just use:

var result = (from t1 in _dbEntities.Charges
              join t2 in _dbEntities.ChargesTypes on t1.ChargesTypeID equals t2.ID
              where t1.StudentID == 1033
              select (int) t2.Ammount).Sum();

Alternatively, you could use the form of Sum which takes a projection, possibly using a different form of Join as you only want the t2 value:

var result = _dbEntities.Charges
                        .Join(_dbEntities.ChargesTypes,
                              t1 => t1.ChargesTypeID,
                              t2 => t2.ID,
                              (t1, t2) => t2)
                        .Sum(t2 => (int) t2.Ammount);

Or even convert in the join and use the "plain" Sum afterwards:

var result = _dbEntities.Charges
                        .Join(_dbEntities.ChargesTypes,
                              t1 => t1.ChargesTypeID,
                              t2 => t2.ID,
                              (t1, t2) => (int) t2.Ammount)
                        .Sum();

EDIT: If the Ammount column (which should be Amount by the way) in the database is an NVARCHAR then a) change it if you possibly can. Life is always simpler if the database types are appropriate; b) use int.Parse if you can't:

var result = (from t1 in _dbEntities.Charges
              join t2 in _dbEntities.ChargesTypes on t1.ChargesTypeID equals t2.ID
              where t1.StudentID == 1033
              select int.Parse(t2.Ammount)).Sum();

If that doesn't work, you may need to do the parsing on the .NET side, e.g.

var result = (from t1 in _dbEntities.Charges
              join t2 in _dbEntities.ChargesTypes on t1.ChargesTypeID equals t2.ID
              where t1.StudentID == 1033
              select t2.Ammount)
             .AsEnumerable() // Do the rest client-side
             .Sum(x => int.Parse(x));