Answer
$ 4\%$
Work Step by Step
$ A=P(1+r)^{t}\qquad$..Substitute $6760$ for $A,\ 6250$ for $P$ and $2$ for $t$.
$ 6760=6250(1+r)^{2}\qquad$..divide both sides by $6250$.
$\displaystyle \frac{6760}{6250}=(1+r)^{2}\qquad$..simplify.
$\displaystyle \frac{676}{625}=(1+r)^{2}$
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{676}{625}}\qquad$..add $-1$ to both sides.
$ 1-1+r=\displaystyle \pm\frac{\sqrt{676}}{\sqrt{625}}-1\qquad$..simplify.
$ r=-\displaystyle \frac{25}{25}\pm\frac{26}{25}\qquad$.. The interest rate cannot be negative, we eliminate the negative solution.
$ r=-\displaystyle \frac{25}{25}+\frac{26}{25}=0.04=4\%$
