You will retire in $41$ years. At that time you will begin making annual withdrawals and the first withdrawal will need to have the purchasing power that $$103,814$ has today. You will withdraw the same amount of money each year of retirement $($and you recognize that its purchasing power will fall as inflation continues$).$ You plan to live for $25$ years during retirement, necessitating $25$ withdrawals. Inflation equals $5\%$ per year. Obviously, you will need to save $($and invest$)$ money to generate the nest egg that will be spent during retirement. The "fund" you plan to invest in earns $8\%$ per year until retirement, and then during retirement it earns $2\%$ per year. How much must you save each year $($with payments into your retirement savings vehicle beginning one year from today$),$ in order to meet your retirement needs?