Two twin brothers have jobs and want to save for retirement. Bill starts at $25$ and goes until he is $70.$ He puts in $$1000$ each quarter into an account that pays $9\%$ compounded quarterly. Jim does not start until $40$ and so he catches up puts in $$2000$ each quarter until he is $70.$

a$.$ Calculate how much each brother has when they retire.

b$.$ Did Jim catch up$?$

c$.$ How much did each make in interest?

d$.$ What would be your advice to someone saving for retirement?

e$.$ Pick one of the brother's and see how much they can withdraw from their account each quarter if they get the same rate and plan to live until $90.$