To determine the Annual Percentage Yield (APY) when the interest rate is 4% and the interest is compounded annually, follow these steps:
1. Understand the formula for APY: The APY formula for interest compounded annually is given by:
[tex]\[
\text{APY} = \left(1 + \frac{r}{n}\right)^n - 1
\][/tex]
where [tex]\( r \)[/tex] is the annual interest rate and [tex]\( n \)[/tex] is the number of compounding periods per year. Since the interest is compounded annually, [tex]\( n = 1 \)[/tex].
2. Substitute the given values:
- The annual interest rate [tex]\( r \)[/tex] is 4%, which is expressed as a decimal by dividing by 100. So, [tex]\( r = 0.04 \)[/tex].
- [tex]\( n = 1 \)[/tex] because the interest is compounded annually.
Plug these values into the APY formula:
[tex]\[
\text{APY} = \left(1 + \frac{0.04}{1}\right)^1 - 1
\][/tex]
3. Simplify the expression:
[tex]\[
\text{APY} = (1 + 0.04) - 1
\][/tex]
[tex]\[
\text{APY} = 1.04 - 1
\][/tex]
[tex]\[
\text{APY} = 0.04
\][/tex]
4. Convert the APY to a percentage: Multiply by 100 to convert the decimal form to a percentage.
[tex]\[
\text{APY Percentage} = 0.04 \times 100 = 4.00\%
\][/tex]
5. Round to 2 decimal places: The APY when rounded to 2 decimal places is 4.00%.
Therefore, the APY for an interest rate of 4% compounded annually is:
[tex]\[
4.00\%
\][/tex]
