Problem $4$:

You get an engineering job when you are $23$ years old with a starting annual salary of $$75,000.$ The company promises a $5\%$ salary increment each year and up to $5\%$ match towards your retirement. Each year you invest $5\%$ of the annual salary in the employer sponsored retirement plan that earns $9\mathrm{.}57\%$ per year compounded monthly to get the $5\%$ employer match.

You decided to retire when you turn $65$ years old. In retirement, there is no additional income except the retirement nest egg that you built when worked for the company. For the first year expenses in retirement, you need $80\%$ of the starting salary $($$$75,000).$ Each subsequent year your expenses increase by $3\%.$ Assuming an effective $4\%$ per year interest during retirement, how many years will your retirement nest egg last? INCLUDE A CASH FLOW DIAGRAM!!