There is a $35\%$ probability that a particular stock will earn a $16\%$ return and a $65\%$ probability that it will earn $10\%.$ What is the risk$-$free rate if the risk premium on the stock is $7\mathrm{.}5\%?$

Question $31$ options:

A$)0\mathrm{.}042$

B$)0\mathrm{.}046$

C$)0\mathrm{.}052$

D$)0\mathrm{.}054$