A $31$ year old employee who has just been hired will contribute part of Their paycheck monthly to a $401(k).$ The employee's starting salary is $$76000$ a year. An annual raise of $4\mathrm{.}29\%$ is given to every employee each year. The employee plans to work for the company until they retire at age $61$ and start withdrawing from their $401(k)30\%$ of their ending salary each year they are retired. The employee expects to be retired for $25$ years. They will withdraw the money in monthly installments. The $401(k)$ earns $7\mathrm{.}72\%$ per year compounded monthly.