find APY corresponding to the given nominal rates. 6.5% compounded quarterly

To calculate the Annual Percentage Yield (APY) from a nominal interest rate compounded quarterly, you can use the following formula:

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

Where:
- \( r \) is the nominal interest rate (as a decimal),
- \( n \) is the number of compounding periods per year.

### Given:
- Nominal interest rate \( r = 6.5\% = 0.065 \),
- Quarterly compounding, so \( n = 4 \).

Now, substitute these values into the formula:

\[
\text{APY} = \left(1 + \frac{0.065}{4}\right)^4 - 1
\]

Let's calculate this.The Annual Percentage Yield (APY) corresponding to a 6.5% nominal interest rate compounded quarterly is approximately **6.66%**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How does the compounding frequency affect APY?
2. What is the APY for the same nominal rate compounded monthly?
3. How do you calculate APY for continuous compounding?
4. What is the difference between APY and nominal interest rate?
5. How would the APY change with semi-annual compounding?

**Tip:** The more frequently interest is compounded, the higher the APY for the same nominal rate.

Learn how to calculate the Annual Percentage Yield (APY) for a 6.5% nominal interest rate compounded quarterly. This problem uses the compound interest formula and covers essential financial math concepts. Suitable for high school students in Grades 10-12.

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