A loan of $$39,200\mathrm{.}00$ at $4\mathrm{.}50\%$ compounded semi$-$annually is to be repaid with payments at the end of every $6$ months. The loan was settled in $6$ years.

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

$$3,511\mathrm{.}41$

$$4,298\mathrm{.}91$

$$3,763\mathrm{.}88$

$$4,062\mathrm{.}55$

b$.$ Calculate the total interest paid.

$$5,966\mathrm{.}56$

$$45,166\mathrm{.}56$

$$2,202\mathrm{.}68$

$$9,730\mathrm{.}44$