The annual interest rate​ r, when compounded more than once a​ year, results in a slightly higher yearly interest rate. This is called the annual​ (or effective) yield and denoted as Y. Find the annual yield as a​ percentage, given the annual interest rate and the compounding frequency.  Annual interest rate of 3.1​%, compounded quarterly  The effective annual yield is  ​(Type an integer or a decimal rounded to the nearest thousandth as​ needed.)

To find the effective annual yield (Y), we use the following formula:

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

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

For this problem:
- \(r = 3.1\%\) or \(0.031\),
- \(n = 4\) (because it's compounded quarterly).

Now, let's calculate the effective annual yield (Y).

\[
Y = \left(1 + \frac{0.031}{4}\right)^4 - 1
\]

Let me compute that for you.The effective annual yield is approximately **3.1%** when the interest rate is 3.1% compounded quarterly.

Would you like further details or have any questions?

Here are some related questions to explore:
1. How does the compounding frequency affect the effective yield?
2. What would be the effective yield if compounded monthly instead of quarterly?
3. How is the effective yield different from the nominal interest rate?
4. What happens to the yield when interest is compounded continuously?
5. How do you calculate the yield for other interest rates like 5% or 7%?

**Tip:** The more frequently interest is compounded, the higher the effective annual yield will be.

The annual interest rate​ r, when compounded more than once a​ year, results in a slightly higher yearly interest rate. This is called the annual​ (or effective) yield and denoted as Y. Find the annual yield as a​ percentage, given the annual interest rate and the compounding frequency. Annual interest rate of 3.1​%, compounded quarterly. The effective annual yield is ​(Type an integer or a decimal rounded to the nearest thousandth as​ needed.)

Learn how to calculate the effective annual yield for an interest rate of 3.1% compounded quarterly. This problem uses the compound interest formula to determine the annual yield as a percentage, suitable for students in Grades 10-12.

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