the equation for compound interest is
[tex]A=P(1+r)^t[/tex]
we will see if it doubles or not
if t=1, we get A=P(1+r)
if t=2, we get A=P(1+r)^2
2(P(1+r))=P(1+r)^2 ?
2(1+r)=(1+r)^2 ?
2+r=r^2+2r+1
etc
when r=-1.618 or 0.618, then it doubles, but not when r is different things
not always
so no, it does not always double the amount of interest earned
