Find the annual percentage yield (APY) in the following situation. A bank offers an APR of \( 3.3 \% \) compounded daily. The annual percentage yield is \( \square \% \). (Do not round until the final answer. Then round to two decimal places as needed.)

To calculate the annual percentage yield (APY) when you have an APR compounded daily, you can use the formula: \[ APY = \left(1 + \frac{r}{n}\right)^{nt} - 1 \] where \( r \) is the annual interest rate (in decimal), \( n \) is the number of compounding periods per year, and \( t \) is the number of years. For your situation: - \( r = 0.033 \) (which is \( 3.3\% \)) - \( n = 365 \) (since it is compounded daily) - \( t = 1 \) Plugging those values into the formula gives: \[ APY = \left(1 + \frac{0.033}{365}\right)^{365 \times 1} - 1 \] Calculating it step-by-step: 1. Calculate \( \frac{0.033}{365} \) which is approximately \( 0.00009041096 \). 2. Calculate \( 1 + 0.00009041096 \) which is approximately \( 1.00009041096 \). 3. Raise this to the power of \( 365 \): \[ (1.00009041096)^{365} \approx 1.03356666989 \] 4. Subtract \( 1 \): \[ 1.03356666989 - 1 \approx 0.03356666989 \] 5. Convert to a percentage by multiplying by \( 100 \): \[ APY \approx 3.356666689 \% \text{ or } 3.36 \% \] Thus, the annual percentage yield (APY) is approximately \( 3.36\% \).