QuestionAugust 4, 2025

Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 3.8% compounded daily. The annual percentage yield is square % (Do not round until the final answer. Then round to two decimal places as needed.)

Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 3.8% compounded daily. The annual percentage yield is square % (Do not round until the final answer. Then round to two decimal places as needed.)
Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 3.8% compounded daily. The annual percentage yield is square % (Do not round until the final answer. Then round to two decimal places as needed.)

Solution
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Answer

3.86\% Explanation 1. Identify the formula for APY The formula for annual percentage yield (APY) is **APY = \left(1 + \frac{r}{n}\right)^n - 1**, where r is the annual interest rate and n is the number of compounding periods per year. 2. Substitute values into the formula Given r = 0.038 (APR of 3.8\%) and n = 365 (compounded daily), substitute these into the formula: **APY = \left(1 + \frac{0.038}{365}\right)^{365} - 1**. 3. Calculate the APY Compute the expression: **APY = \left(1 + \frac{0.038}{365}\right)^{365} - 1 \approx 0.03864**. 4. Convert to percentage Convert the decimal to a percentage by multiplying by 100: **APY \approx 3.864\%**. 5. Round to two decimal places Round 3.864\% to two decimal places: **3.86\%**.

Explanation

1. Identify the formula for APY<br /> The formula for annual percentage yield (APY) is **APY = \left(1 + \frac{r}{n}\right)^n - 1**, where $r$ is the annual interest rate and $n$ is the number of compounding periods per year.<br /><br />2. Substitute values into the formula<br /> Given $r = 0.038$ (APR of $3.8\%$) and $n = 365$ (compounded daily), substitute these into the formula: **APY = \left(1 + \frac{0.038}{365}\right)^{365} - 1**.<br /><br />3. Calculate the APY<br /> Compute the expression: **APY = \left(1 + \frac{0.038}{365}\right)^{365} - 1 \approx 0.03864**.<br /><br />4. Convert to percentage<br /> Convert the decimal to a percentage by multiplying by 100: **APY \approx 3.864\%**.<br /><br />5. Round to two decimal places<br /> Round $3.864\%$ to two decimal places: **3.86\%**.
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