Answer
$6.82\%$
Work Step by Step
The formula for effective rate of interest ($r_e$), where $i$ is the given nominal rate, $n$ is the number of compounding periods per year, is
$r_e=(1+\frac{i}{n})^n-1$
Thus,
$0.07=(1+\frac{i}{4})^4-1\\
0.07+1=\left(1+\frac{i}{4}\right)^4-1+1\\
1.07=\left(1+\frac{i}{4}\right)^4\\
\sqrt[4]{1.07}=\sqrt[4]{\left(1+\frac{i}{4}\right)^4}\\
\sqrt[4]{1.07}=1+\frac{i}{4}\\
\sqrt[4]{1.07}-1=\frac{i}{4}\\
4(\sqrt[4]{1.07}-1)=i$
Use a calculator to obtain
$i=0.06823410001\\
i\approx 6.82\%$
