Currently, at age $29$ you are entering the job market. You wish to retire at the age of $65$ and your projected life span is to live until age $83.$ You figure that you can live comfortably on $$85,000$ per year during your years of retirement. Current market rates indicate that you should be able to earn $7\mathrm{.}5\%$ interest per year.

a$.$ How much money will you need to accumulate by the age of $65$ to provide you with an $$85,000$ annuity until you expect to die?

b$.$ How much money will you need to save each year during your career in order to accumulate the amount computed in part a$.$ above?