You live in a world with three securities A$,$ B$,$ and C$.$ You are provided with the following risk$-$return profile for the risky securities$.$ Additionally, the correlation between securities A and B is $0\mathrm{.}0,$ between securities A and C$,$ is $0\mathrm{.}0,$ and between securities B and C$$ is $-1\mathrm{.}0.$

SecurityExpected ReturnsStandard DeviationA$15\%20\%$B$18\%30\%$C$8\mathrm{.}0\%19\%$

What is the implied risk$-$free rate if there are no arbitrage opportunities?$$

Carry forward at least four decimal places and report your answer in percentage points up to $2$ decimal places $($example $4\mathrm{.}10).$