Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 1.12% compounded quarterly. The annual percentage yield is ____% (Do not round until the final answer. Then round to two decimals places as needed.)

To calculate the Annual Percentage Yield (APY), we use the following formula:

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

Where:
- \(r\) is the annual percentage rate (APR) expressed as a decimal.
- \(n\) is the number of compounding periods per year.

In this problem:
- \(r = 1.12\% = 0.0112\)
- \(n = 4\) (since it's compounded quarterly)

Now let's calculate the APY:

\[
APY = \left( 1 + \frac{0.0112}{4} \right)^4 - 1
\]

I will calculate this step-by-step.

The Annual Percentage Yield (APY) is 1.12%.

Do you want further details or have any questions?

Here are 5 related questions to expand on this:
1. How does compounding frequency affect APY?
2. How would the APY change if the APR were compounded monthly instead of quarterly?
3. Can you calculate the APY if the APR were 2% compounded annually?
4. What is the difference between APR and APY in financial terms?
5. How can an investor use APY to compare different savings accounts?

**Tip:** Always remember that increasing the compounding frequency generally increases the APY, even if the APR remains the same.

Learn how to calculate the Annual Percentage Yield (APY) for a bank offering an APR of 1.12% compounded quarterly. This problem involves key financial math concepts like compounding and exponential growth, with a step-by-step solution. Suitable for high school and college students.

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