An account has a rate of 4.2%. Find the effective annual yield if the 
interest is compounded 1000 times per year. What is the effective annual
 yield? (round to the nearest hundredth as needed)

The formula for the effective annual yield (EAY) when interest is compounded \(n\) times per year is:

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

Where:
- \( r \) is the nominal annual interest rate (4.2% or 0.042 in decimal form),
- \( n \) is the number of times the interest is compounded per year (1000 in this case).

Now, let's plug in the values and calculate:

\[
\text{EAY} = \left( 1 + \frac{0.042}{1000} \right)^{1000} - 1
\]

I'll calculate this next.

The effective annual yield (EAY), when compounded 1000 times per year at a nominal rate of 4.2%, is approximately 4.29%.

Do you want further details or have any questions?

Here are 5 related questions to expand on this concept:
1. How does the effective annual yield change if compounded daily instead of 1000 times per year?
2. What is the difference between nominal and effective interest rates?
3. How is the effective annual yield affected by increasing the compounding frequency to infinity?
4. What would the effective annual yield be for a nominal interest rate of 5% compounded quarterly?
5. What happens to the yield if the interest rate drops to 3% but is still compounded 1000 times?

**Tip:** The more frequently interest is compounded, the closer the effective yield approaches the continuous compounding limit.

An account has a rate of 4.2%. Find the effective annual yield if the interest is compounded 1000 times per year. What is the effective annual yield? (round to the nearest hundredth as needed)

Learn how to calculate the effective annual yield for an account with a nominal interest rate of 4.2%, compounded 1000 times per year. This example uses the compound interest formula to find the EAY, providing a step-by-step solution suitable for high school students in Grades 10-12.

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