Find the annual percentage yield​ (APY) in the following situation.
A bank offers an APR of 4.59​% compounded quarterly.
The annual percentage yield is ______.  (Do not round until the final answer. Then round to two decimal places as​ needed.)

To calculate the annual percentage yield (APY) when given the annual percentage rate (APR) and the compounding frequency, we can use the following formula:

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

Where:
- \(r\) is the annual percentage rate (APR) in decimal form,
- \(n\) is the number of compounding periods per year.

Given:
- APR = 4.59% = 0.0459,
- The compounding frequency is quarterly, so \(n = 4\).

Now, we can plug these values into the formula and solve for APY.

\[
\text{APY} = \left(1 + \frac{0.0459}{4}\right)^4 - 1
\]

Let me calculate that for you.The annual percentage yield (APY) is 4.67%.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How would the APY change if the interest was compounded monthly instead of quarterly?
2. What would the APY be for an APR of 5.25% compounded annually?
3. How does the number of compounding periods affect the APY?
4. Can you calculate the APY for continuous compounding given an APR of 4.59%?
5. What is the difference between APR and APY in terms of practical use?

**Tip:** The more frequently interest is compounded, the higher the APY will be, even if the APR remains the same.

Find the annual percentage yield​ (APY) in the following situation. A bank offers an APR of 4.59% compounded quarterly. The annual percentage yield is ______. (Do not round until the final answer. Then round to two decimal places as​ needed.)

Learn how to calculate the annual percentage yield (APY) for an APR of 4.59% compounded quarterly. This problem explains key financial math concepts such as interest calculation and uses the APY formula. Suitable for students in Grades 10-12.

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