RESP with deposited $$150$ into a fund at the beginning of every quarter for $12$ years. She then stopped making deposits into the fund and allowed the investment to grow for $4$ more years. The fund was growing at $3\mathrm{.}20\%$ compounded quarterly.

$(50$ points$)$

a$.$ What was the accumulated value of the fund at the end of year $12?$

b$.$ How much can the son withdraw at the beginning of every six$-$month period for the four years that he is in college?