Microsoft stock$$s beta is $1\mathrm{.}5.$ According to CAPM, the stock has an expected return rate of $13\mathrm{.}5\%.$

$1)$ If the expected return of the S&P $500$ Index is $10\%,$ what is the risk$-$free rate? $(4$ points$)$

$2)$ Given your answer in $1),$ if General Mills stock has a beta of $0\mathrm{.}7,$ what is the expected return of the stock? $(3$ points$)$

$3)$ If you are constructing a portfolio of $$100,000$ using both Microsoft and General Mills stocks, and your goal is to have a portfolio beta $1\mathrm{.}2,$ how much money would you invest in Microsoft?