## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$6.823 \%$
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 $r_e = 0.07$ $\text{Compounded quarterly} \to n = 4$ $0.07 = \left(1+\dfrac{r}{4} \right)^4 -1$ $0.07+1 = \left(1+\dfrac{r}{4} \right)^4$ $1.07 = \left(1+\dfrac{r}{4} \right)^4$ $\left(1+\dfrac{r}{4} \right) = \sqrt[4]{1.07}$ $\dfrac{r}{4} = \sqrt[4]{1.07}-1$ $r = 4(\sqrt[4]{1.07}-1)$ $r \approx 0.06823$ $r = \boxed{6.823 \%}$