To compute the Annual Percentage Yield (APY) for a savings account that earned [tex]$38.25 in interest on an initial deposit of $[/tex]850 over the past 365 days, follow these steps:
1. Calculate the Interest Rate:
The interest rate can be determined by dividing the interest earned by the initial deposit.
[tex]\[
\text{Interest Rate} = \frac{\text{Interest Earned}}{\text{Initial Deposit}}
\][/tex]
Plugging in the values given:
[tex]\[
\text{Interest Rate} = \frac{38.25}{850} = 0.045
\][/tex]
2. Calculate the Annual Percentage Yield (APY):
The APY takes into account the effect of compounding interest over a year. Since the interest was earned over a full year (365 days), the APY can be calculated using the following formula:
[tex]\[
\text{APY} = \left(1 + \text{Interest Rate}\right)^{\frac{365}{\text{Days}}} - 1
\][/tex]
Given that the number of days is 365:
[tex]\[
\text{APY} = \left(1 + 0.045\right)^{\frac{365}{365}} - 1 = \left(1 + 0.045\right)^1 - 1 = 0.045
\][/tex]
3. Convert the APY to a Percentage:
To express the APY as a percentage, multiply by 100 and round to 2 decimal places.
[tex]\[
\text{APY Percentage} = 0.045 \times 100 = 4.50\%
\][/tex]
Therefore, the Annual Percentage Yield (APY) for the savings account is 4.50%.
