Jake just turned $20$ years old, and he wants to save $$3$ a day for his retirement. Every day he places $$3$ in a drawer. At the end of each year, he invests the accumulated money $($$$1,095)$ in a savings account with an annual return of $12\%.$

$1)$ How much money will he have when he turns $65$ years old?

$2)$ His same year old friend, Bill, starts saving when he becomes $40$ years old. How much will Bill have when he turns $65$ years old?

$3)$ How much must Bill despoit annually to catch Mike when they become $65$ years old?

$4)$ If Mike puts $$3$ in a savings account every day with an expected annual return of $12\%,$ compounded daily. How much money will he have when he is $65$ years old?