Answer
Better deal: $ 6\displaystyle \frac{1}{4}\%$ compounded annually.
Work Step by Step
Apply the Effective Rate of Interest Theorem:
The effective rate of interest $r_{e}$ of an investment earning an annual interest rate $r$ is given by
Compounding $n$ times per year: $\displaystyle \quad r_{e}=\left(1+\frac{r}{n}\right)^{n}-1$
Continuous compounding: $\quad \quad r_{e}=e^{r}-1$
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We compare the effective rates. The larger $r_{e}$ represents the better deal.
$ 6\%$ compounded quarterly:
$r_{e}=\displaystyle \left(1+\frac{0.06}{4}\right)^{4}-1\approx 0.061363551$
$ 6\displaystyle \frac{1}{4}\%$ compounded annually:
$r_{e}=\displaystyle \left(1+\frac{0.0625}{1}\right)^{1}-1=0.625$
Better deal: $ 6\displaystyle \frac{1}{4}\%$ compounded annually.
