Sasha predicts that she will need $$24000$ to remodel her carpentry workshop in $6$ years. She has found three investment options to consider:

A$.4\mathrm{.}80\%,$ compounded annually

B$.4\mathrm{.}75\%,$ compounded semi$-$annually

C$.4\mathrm{.}70\%,$ compounded quarterly

a$)$ Compare the rates of return for these three options. Which option should she choose? Why?

b$)$ How much interest will she earn?