Answer
$11\frac{3}{4}$ years
Work Step by Step
Using the formula $A=P(1+\frac{r}{n})^{nt}$, we substitute in the values from the problem such that:
$2000 = 1000(1+\frac{0.06}{4})^{4t}$
The equation is rearranged to make t the subject:
$2 = (1+\frac{0.06}{4})^{4t} = (1.015)^{4t} $
$\log 2 = \log (1.015)^{4t}$
$\log 2 = 4t(\log 1.015)$
$4t = \frac{\log2}{\log 1.015}$
$t = \frac{\frac{\log2}{\log 1.015}}{4} \approx 11\frac{3}{4}$
