Problem $11-31$ Beta and CAPM

A portfolio that combines the risk$-$free asset and the market portfolio has an expected return of $7\mathrm{.}8$ percent and a standard deviation of $10\mathrm{.}8$ percent. The risk$-$free rate is $4\mathrm{.}8$ percent, and the expected return on the market portfolio is $12\mathrm{.}8$ percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a $\mathrm{.}53$ correlation with the market portfolio and a standard deviation of $55\mathrm{.}8$ percent? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

Expected rate of return