Answer
$ 10\%$
Work Step by Step
$ A=P(1+r)^{t}\qquad$..Substitute $2420$ for $A,\ 2000$ for $P$ and $2$ for $t$.
$ 2420=2000(1+r)^{2}\qquad$..divide both sides by $2000$.
$\displaystyle \frac{2420}{2000}=(1+r)^{2}\qquad$..simplify.
$\displaystyle \frac{121}{100}=(1+r)^{2}$
According to the general principle of square roots:
For any real number $k$ and any algebraic expression $x$ :
$\text{If }x^{2}=k,\text{ then }x=\sqrt{k}\text{ or }x=-\sqrt{k}$.
$ 1+r=\pm\sqrt{\frac{121}{100}}\qquad$..add $-1$ to both sides.
$ 1-1+r=\displaystyle \pm\frac{\sqrt{121}}{\sqrt{100}}-1\qquad$..simplify.
$ r=-1\displaystyle \pm\frac{11}{10}\qquad$.. The interest rate cannot be negative, we eliminate the negative solution.
$ r=-1+\displaystyle \frac{11}{10}=0.1=10\%$
