Peter made periodic deposits into a savings account at the end of every month for $3$ years. The investments were earning $7\mathrm{.}20\%$ compounded quarterly and grew to $$12,375\mathrm{.}00$ at the end of $3$ years.

a$.$ Calculate the size of the month$-$end deposits.

$$319\mathrm{.}00$

$$309\mathrm{.}19$

$$247\mathrm{.}30$

$$299\mathrm{.}90$

b$.$ How long will it take for the $$12,375\mathrm{.}00$ to accumulate to $$39,815\mathrm{.}00$ if the interest rate remained the same and he continued making the same month$-$end deposits throughout the term?

$6$ years and $0$ months

$8$ years and $0$ months

$5$ years and $0$ months

$5$ years and $3$ months