Question $1(14$ marks$)$

Susan worked part$-$time jobs during her teenage years to save for her living expenses during college life. Today is her ${18}^{th}$ birthday, and she is about to begin her college studies.

Susan is proud of herself that the jobs she worked as a teenager allowed her to save a total of $$100,000$ at the age of $18.$ The money will be invested in a financial asset at $12\%$ compounded monthly. As a full$-$time student, Susan is going to rely solely on her savings for all the living expenses during the four years at college. She expects to graduate on her ${22}^{sd}$ birthday.

$($a$)$ How much can Susan withdraw every month from her total saving of $$100,000$ while she is in college if the first withdrawal occurs today and the last withdrawal occurs I month before her ${22}^{nd}$ birthday?

$(5$ marks$)$

$($b$)$ How much can Susan withdraw every month from her total saving of $$100,000$ while she is in college if she waits until the end of this month to make the first withdrawal and the last withdrawal occurs on her ${22}^{nd}$ birthday?

$(4$ marks$)$

$($c$)$ How much can Susan withdraw every month from her total saving of $$100,000$ if she waits until the end of the thirteenth month to make the first withdrawal and last withdrawal occur on her ${22}^{nd}$ birthday?

$(5$ marks$)$