Answer
It takes 17 years for $\$2100$ deposited at $\%4$ compounded quarterly to double.
And takes 28 years for $\$2100$ deposited at $\%4$ compounded quarterly to triple.
Work Step by Step
Use the formula for compound interest with
$P=\$2100$
$r=0.04$
$m=4$
To double:
$A=P(1+\frac{r}{m})^{tm}$
$42000=2100(1+\frac{0.04}{4})^{4t}$
$(1+\frac{0.04}{4})^{4t}=2$
$4t=\log_{1.01}2$
$4t = 69.66$
$t \approx 17.42 \approx 17$
To triple:
$A=P(1+\frac{r}{m})^{tm}$
$6300=2100(1+\frac{0.04}{4})^{4t}$
$(1+\frac{0.04}{4})^{4t}=3$
$4t=\log_{1.01}3$
$4t = 110.41$
$t \approx 27.6\approx 28$
