Karina has a $$20,000$ portfolio, which is invested in Stocks A and B$,$ and a risk$-$free asset. $$8,000$ is invested in Stock A$.$ Stock A has a beta of $1\mathrm{.}75,$ and Stock B has a beta of $1\mathrm{.}10.$ How much needs to be invested in Stock B if Karina wants a portfolio beta of $1\mathrm{.}20?(10\%)$

A$.$ $$10,000\mathrm{.}00$

B$.$ $$9090\mathrm{.}91$

C$.$ $$8000\mathrm{.}00$

D$.$ $$7,500\mathrm{.}00$

E$.$ $$6,818\mathrm{.}18$