To find the effective annual rate (EAR) when interest is compounded continuously, we can use the formula:
\[ \text{EAR} = e^r - 1 \]
where \( r \) is the nominal interest rate (in decimal form), and \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
Given that the bank offers a 6.00% interest rate, we can convert this percentage to a decimal:
\[ r = 6.00% = 0.06 \]
Now we can apply the formula for EAR:
\[ \text{EAR} = e^{0.06} - 1 \]
Calculating \( e^{0.06} \):
\[ e^{0.06} \approx 1.061837 \]
Now, substituting back into the EAR formula:
\[ \text{EAR} \approx 1.061837 - 1 \approx 0.061837 \]
Converting back to percentage form:
\[ \text{EAR} \approx 0.061837 \times 100% \approx 6.1837% \]
Thus, the effective annual rate when interest is compounded continuously is approximately:
\[ \boxed{6.18%} \]