Lynn is $22$ years old and just began to work at Hewett. Lynn$\text{'}$s salary is $$40,000$ and plans to contribute $10\%$ of her salary to her $401k$ which currently has Lynn plans to retire at $62$ and anticipates raise in her salary of $1\%$ each year.

The anticipated rate of return for the $401k$ is $5\%.$ The employer will match $100\%$ of what the employee contributes but with a salary limit for the match at How much will Lynn contribute during her $40$ years of employment? $($This is the total employee contributions$).$ Round to the nearest cent.