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

$7.9 \% \text{ compounded daily}$
The rate with the highest effective rate of interest represents the better deal For $r_1 = 8\%=0.08$, $\text{compounded semiannually} \to n_1 = 2$ $r_{e_1} = \left(1+\dfrac{r_1}{n_1} \right)^{n_1} - 1$ $r_{e_1} = \left(1+\dfrac{0.08}{2} \right)^{2} - 1$ $r_{e_1} = 0.0816$ For $r_2 = 7.9\%=0.079$, $\text{compounded daily} \to n_2 = 365$ $r_{e_2} = \left(1+\dfrac{r_2}{n_2} \right)^{n_2} - 1$ $r_{e_2} = \left(1+\dfrac{0.079}{365} \right)^{365} - 1$ $r_{e_2} \approx 0.082195$ Since $r_{e2} > r_{e1}$, then $7.9\%$ compounded daily is the better deal.