The formula for an Ordinary Annuity saving account compounded quarterly  is


    FV = 


where FV is the future value, P is the annual payment at the end of each year, n is the number of compounding periods.


So, we need to find " r " from the equation


     =  =  = 2.08.


Multiply both sides by .  You will get


     = .  


For brevity, introduce new variable x =  and write this equation in the form


     = 1 + 2.08x.


Simplify

    1 + 2x + x^2 = 1 + 2.08x

    x^2 - 0.08x = 0

    x*(x-0.08) = 0.


Of two roots, x= 0 and x= 0.08, only positive root makes sense.


So, x = 0.08;  hence  r= 4x = 4*0.08 = 0.32.


ANSWER.  Annual interest rest should be 0.32, or 32%.


CHECK.   = 5200  dollars.    ! Correct !