Suppose you observe the following situation:

Security Beta Expected Return

Pete Corp. 1.25 . 1323
Repete Co. .87 .0967

a. Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e. g., 32.16.)
b. What is the risk-free rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.)

a. The expected return on the market is 10.89%

b. The risk-free rate is 1.52%

Explanation:

In order to calcuate the expected return on the market and the he risk-free rate we would have to use the following formulas:

Expected return=risk-free rate +Beta*(market rate- risk-free rate )

13.23=Rf+1.25*(Rm-Rf)

13.23=1.25Rm-0.25Rf

Rm=(13.23+0.25Rf)/1.25

To calculate the risk free rate, we use the following:

9.67=Rf+0.87*(Rm-Rf)

9.67=0.13Rf+0.87Rm

9.67=0.13Rf+0.87*(13.23+0.25Rf)/1.25

9.67=0.13Rf+9.20808+0.174Rf

Rf=(9.67-9.20808)/(0.13+0.174)

=1.52%(Approx)=risk free rate

Rm=(13.23+0.25Rf)/1.25

=10.89%(Approx)=market rate

you have to put the parentheses like this:

in fact, you have to perform the operation inside parentheses first, and then proceed in order: