The effective annual rate with continuous compounding = eʳ − 1 = e⁰.⁰⁹ − 1 = 0.09417, or 9.42%.

Explanation:

When interest is compounded continuously, the formula for the effective annual rate (EAR) is:

EAR = eʳ - 1

Where:

• e is the mathematical constant approximately equal to 2.71828
• r is the stated annual interest rate (9% = 0.09)

Plugging in the values: EAR = e⁰.⁰⁹ - 1 EAR = 1.094174 - 1 EAR = 0.094174 or 9.4174%

Rounded to two decimal places, this is 9.42%.

Why other options are incorrect:

• Option B (9.67%): This would be the EAR for a higher rate or different compounding frequency.
• Option C (9.20%): This is lower than the stated rate, which cannot be correct for continuous compounding since continuous compounding always yields a higher effective rate than the stated rate.