Answer
$5.827 \%$
Work Step by Step
Effective Rate of Interest Formula for Continuous Compounding
$$r_e = e^r-1$$
$r_e:$ Effective Rate of Interest
$r:$ Annual Interest Rate
$r_e = 0.06$
$0.06 = e^r -1$
$0.06+1 = e^r$
$1.06 = e^r$
Taking the natual logarithm of both sides
$\ln{1.06} = \ln{e^r}$
$\ln{1.06} = r \ln{e}$
$\because \ln{e} = 1$
$\therefore \ln{1.06} = r$
$r \approx 0.05827$
$r = \boxed{5.827 \% }$
