A mutual fund manager has a $$350$ million portfolio with a beta of $1\mathrm{.}10.$ The risk$-$free rate is $3\mathrm{.}5\%,$ and the market risk premium is $6\mathrm{.}00\%.$ The manager expects to receive an additional $$150$ million which she plans to invest in several different stocks. After investing the additional funds, she wants to reduce the portfolio$$s risk level so that once the additional funds are invested the portfolio$$s required return will be $9\mathrm{.}20\%.$ What must the average beta of the new stocks added to the portfolio be $($not the new portfolio$$s beta$)$ to achieve the desired required rate of return?

a$.0\mathrm{.}5000$

b$.0\mathrm{.}5500$

c$.0\mathrm{.}6000$

d$.0\mathrm{.}7500$

e$.0\mathrm{.}9500$