A loan of $$27,500\mathrm{.}00$ at $3\mathrm{.}50\%$ 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.

$$2,383\mathrm{.}50$

$$2,845\mathrm{.}81$

$$2,560\mathrm{.}63$

$$2,770\mathrm{.}09$

b$.$ Calculate the total interest paid.

$$3,227\mathrm{.}56$

$$30,727\mathrm{.}56$

$$666\mathrm{.}93$

$$5,788\mathrm{.}19$