Joe estimates that his daughter's college needs, beginning in $8$ years, will be $$3100$ at the end of each quarter for $4$ years. $($a$)$ Find the total amount needed in $8$ years, assuming $6\%$ compounded quarterly. $($b$)$ Will he have enough money available in $8$ years if he invests $$1100$ at the end of each quarter for the next $8$ years at $6\%$ compounded quarterly?

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$($a$)$ The total amount needed in $8$ years is approximately $$43806\mathrm{.}91.$

$($Round to the nearest cent as needed.$)$

$($b$)$ If Joe invests $$1100$ at the end of each quarter for $8$ years, will he have enough money?

No

Yes