Answer
$6.823 \%$
Work Step by Step
Effective Rate of Interest Formula
$$r_e = \left(1+\dfrac{r}{n} \right)^n - 1$$
$r_e:$ Effective Rate of Interest
$r:$ Annual Interest Rate
$n:$ Number of compoundings per year
$r_e = 0.07$
$\text{Compounded quarterly} \to n = 4$
$0.07 = \left(1+\dfrac{r}{4} \right)^4 -1$
$0.07+1 = \left(1+\dfrac{r}{4} \right)^4$
$1.07 = \left(1+\dfrac{r}{4} \right)^4$
$\left(1+\dfrac{r}{4} \right) = \sqrt[4]{1.07}$
$\dfrac{r}{4} = \sqrt[4]{1.07}-1$
$r = 4(\sqrt[4]{1.07}-1)$
$r \approx 0.06823$
$r = \boxed{6.823 \%} $
