SOLUTION: Suppose that a savings account pays an effective rate of interest of 9.3 percent. What is the equivalent semiannual compound interest rate

It is reduced to solving this quadratic equation


    1.093 = (1 + r/2)^2.


In other words, they want you find the solution r to this quadratic equation.


Simplify it


    1.093 = 1 + r + 

    0.093 = r + 

    4*0.093 = 4r + r^2

    r^2 + 4r - 0.372 = 0


Use the quadratic formula and get the solution.


Of the two possivle roots, one is positive, the other is negative.


Choose the positive root  r = 0.09093...,  or r = 0.09  (rounded).


ANSWER.  The rounded equivalent semiannual compound interest rate is 0.09, or 9%.


CHECK.   = 1.0920, which is close enough.