Answer
It takes 11 years for $\$1000$ deposited at $\%6$ compounded semiannually to double.
And takes 11 years for $\$1000$ deposited at $\%6$ compounded semiannually to triple.
Work Step by Step
Use the formula for compound interest with
$P=\$1000$
$r=0.06$
$m=2$
To double:
$A=P(1+\frac{r}{m})^{tm}$
$2000=1000(1+\frac{0.06}{2})^{2t}$
$(1+\frac{0.06}{2})^{2t}=2$
$2t=\log_{1.03}2$
$2t = 23.45$
$t \approx 11.72 \approx 11$
To triple:
$A=P(1+\frac{r}{m})^{tm}$
$3000=1000(1+\frac{0.06}{2})^{2t}$
$(1+\frac{0.06}{2})^{2t}=3$
$2t=\log_{1.03}3$
$2t =37.167$
$t \approx 18.58 \approx 18$
