To calculate the effective annual rate (EAR) when interest is compounded continuously, you can use the formula:
\[ \text{EAR} = e^{r} - 1 \]
where \( r \) is the nominal interest rate (expressed as a decimal) and \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
Given that the nominal interest rate is 9.00% (or 0.09 in decimal form), we can plug this value into the formula:
\[ \text{EAR} = e^{0.09} - 1 \]
Now calculate \( e^{0.09} \):
\[ e^{0.09} \approx 1.09417 \]
Now, subtract 1:
\[ \text{EAR} \approx 1.09417 - 1 \approx 0.09417 \]
To express this as a percentage, multiply by 100:
\[ \text{EAR} \approx 9.42% \]
Therefore, the effective annual rate if interest is compounded continuously is approximately 9.42%.