Answer
$ 5.827\%$
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 continuously, given $r_{e}=0.06,$
$0.06=e^{r}-1\qquad.../+1$
$1.06=e^{r}\qquad.../\ln(...)$
$\ln 1.06=r$
$r\approx 0.05827$
$ r\approx 5.827\%$
