A loan of $$34,500\mathrm{.}00$ at $5\mathrm{.}50\%$ compounded semi$-$annually is to be repaid with payments at the end of every $6$ months. The loan was settled in $5$ years.

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

$$3,677\mathrm{.}23$

$$4,577\mathrm{.}04$

$$3,993\mathrm{.}02$

$$4,379\mathrm{.}46$

b$.$ Calculate the total interest paid.

$$5,430\mathrm{.}20$

$$39,930\mathrm{.}20$

$$1,437\mathrm{.}18$

$$9,423\mathrm{.}22$