A mutual fund manager has a $$450$ million portfolio with a beta of $1\mathrm{.}20.$ The risk$-$free rate is $2\mathrm{.}5\%,$ and the market risk premium is $5\mathrm{.}00\%.$ The manager expects to receive an additional $$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 $7\mathrm{.}50\%.$ 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$.0\mathrm{.}4000$

b$.0\mathrm{.}5500$

c$.0\mathrm{.}7000$

d$.0\mathrm{.}8500$

e$.1\mathrm{.}0000$