Answer
$ 6.823\%$
Work Step by Step
The amount A after t years due to a principal P Apply the 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: $r_{e}=\displaystyle \left(1+\frac{r}{n}\right)^{n}-1$
Continuous compounding: $\quad r_{e}=e^{r}-1$
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Compounding $n=4$ times per year, given $r_{e}=0.07,$
$0.07=\displaystyle \left(1+\frac{r}{4}\right)^{4}-1\qquad.../+1$
$1.07=\displaystyle \left(1+\frac{r}{4}\right)^{4}\qquad.../(...)^{1/4}$
$1.07^{1/4}=1+\displaystyle \frac{r}{4}\qquad.../-1$
$\displaystyle \frac{r}{4}=1.07^{1/4}-1$
$r=4(1.07^{1/4}-1)\approx 0.06823$
$ r\approx 6.823\%$
