You have been managing a $$900,000$ portfolio that has a beta of $1\mathrm{.}50$ and a required rate of return of $15\%.$ The current risk$-$free rate is $3\mathrm{.}00\%.$ Assume that you receive another $$100,000.$ If you invest the money in a stock with a beta of $0\mathrm{.}40,$ what will be the required return on your million dollar portfolio?

$12\mathrm{.}708\%$

$14\mathrm{.}826\%$

$13\mathrm{.}414\%$

$14\mathrm{.}120\%$

$15\mathrm{.}532\%$