Assuming the return is compounded annually, the multiplier each year for rate "r" is (1+r). Then the multiplier for "t" years is (1+r)^t. We want this to be 2.
... 2 = (1+r)^t
... log(2) - t·log(1+r)
... log(2)/log(1+r) = t
The attachment shows the rounded calculator result for r={4%, 10%, 13%}.