A loan of $$31,700\mathrm{.}00$ at $7\mathrm{.}00\%$ compounded semi$-$annually is to be repaid with payments at the end of every $6$ months. The loan was settled in $4$ years.

a$.$ Calculate the size of the periodic payment.

$$4,166\mathrm{.}84$

$$5,308\mathrm{.}73$

$$4,611\mathrm{.}61$

$$5,184\mathrm{.}36$