Suppose that you are currently $21$ years old and expect to retire from work when you are $65$ years old. Once retired, you expect to live until you are $90$ years old. You anticipate that you will need $$80,000$ per year when retired to maintain your standard of living. Assuming that you can save at an interest rate of $8\mathrm{.}00\%$ while working and an interest rate of $3\mathrm{.}00\%$ while retired, determine the following values:

A$.$ The amount you will need to save by the time you retire to meet your needs in retirement and

B$.$ The annual amount that you will need to save each year while you are working to have enough saved by the time you retire

Note: For the purposes of this question you can assume that all cash flows $($e$.$g$.,$ deposits and withdrawals from the retirement savings account$)$ occur at the end of each year.