You want your portfolio beta to be $1\mathrm{.}6.$ Currently, the portfolio consists of $$200,000$ invested in stock A with a beta of $1\mathrm{.}5$ and $$400,000$ in stock B with a beta of $\mathrm{.}8.$ You have another $$400,000$ to invest and want to divide it between stock C with a beta of $2\mathrm{.}1$ and stock A $($in which you are already invested; you are adding to stock A$).$ How much should you invest in stock C$?$

Group of answer choices

$$200,000$

$$150,000$

$$300,000$

$$100,000$