Questions: Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 6.9% compounded daily. The annual percentage yield is %. (Do not round until the final answer. Then round to two decimal places as needed.)

Solution Steps

To find the annual percentage yield (APY) given an annual percentage rate (APR) compounded daily, we can use the formula:

\[ \text{APY} = \left(1 + \frac{\text{APR}}{n}\right)^n - 1 \]

where \( n \) is the number of compounding periods per year. For daily compounding, \( n = 365 \).

1. Convert the APR from a percentage to a decimal.
2. Use the formula for APY with daily compounding.
3. Convert the result back to a percentage and round to two decimal places.

The annual percentage rate (APR) is given as \( 6.9\% \). To convert this to a decimal, we calculate: \[ APR_{\text{decimal}} = \frac{6.9}{100} = 0.069 \]

Using the formula for annual percentage yield (APY) with daily compounding: \[ APY = \left(1 + \frac{APR_{\text{decimal}}}{n}\right)^n - 1 \] where \( n = 365 \): \[ APY = \left(1 + \frac{0.069}{365}\right)^{365} - 1 \approx 0.0714292222327868 \]

To express the APY as a percentage, we multiply by 100 and round to two decimal places: \[ APY_{\text{percentage}} = 0.0714292222327868 \times 100 \approx 7.14\% \]

Final Answer