Answer
$5.83\%$
Work Step by Step
The formula for the effective rate of interest ($r_e$) for the continuous compounding case, where $r$ is the given annual interest rate, is given by:
$r_e=e^r-1$
Thus, here we have
$0.06=e^r-1\\
0.06+1=e^r\\
1.06=e^r$
Take the natural log of both sides to obtain
$\ln{1.06}=\ln{e^r}\\
\ln{1.06}=r\ln{e}\\
\ln{1.06}=r(1)\\
\ln{1.06}=r\\
0.05826890812=r\\
r\approx5.83\%$
