To calculate the effective annual rate (EAR) when interest is compounded continuously, we can use the formula:
\[ \text{EAR} = e^r - 1 \]
where \( e \) is Euler's number (approximately 2.71828), and \( r \) is the annual nominal interest rate (expressed as a decimal).
Given that the nominal interest rate is 8.00%, we first convert this to decimal form:
\[ r = 0.08 \]
Now we can substitute \( r \) into the formula:
\[ \text{EAR} = e^{0.08} - 1 \]
Calculating \( e^{0.08} \):
\[ e^{0.08} \approx 1.08328706767 \]
Now, subtracting 1 from this value:
\[ \text{EAR} \approx 1.08328706767 - 1 \approx 0.08328706767 \]
Finally, converting this back to a percentage:
\[ \text{EAR} \approx 0.0833 \times 100 \approx 8.33% \]
Thus, the effective annual rate (EAR) when interest is compounded continuously at 8.00% is approximately 8.33%.