Find the annual percentage yield for an investment at the following rate. 6.8% compounded monthly

To find the annual percentage yield (APY) for an investment compounded monthly at a nominal interest rate of 6.8%, we can use the formula:

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

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

For this problem:
- \( r = 0.068 \),
- \( n = 12 \) (since it's compounded monthly),
- \( t = 1 \) (to find the yield for one year).

Plugging in the values:

\[
APY = \left(1 + \frac{0.068}{12}\right)^{12 \times 1} - 1
\]

Calculating it step by step:

1. Calculate \( \frac{0.068}{12} \):
   \[
   \frac{0.068}{12} \approx 0.00566667
   \]

2. Calculate \( 1 + 0.00566667 \):
   \[
   1 + 0.00566667 \approx 1.00566667
   \]

3. Raise it to the power of 12:
   \[
   (1.00566667)^{12} \approx 1.071946
   \]

4. Subtract 1:
   \[
   1.071946 - 1 \approx 0.071946
   \]

5. Convert to percentage:
   \[
   APY \approx 0.071946 \times 100 \approx 7.19\%
   \]

Thus, the annual percentage yield (APY) for an investment at a 6.8% nominal interest rate compounded monthly is approximately **7.19%**.

If you need more details or have any questions, feel free to ask! Here are some related questions you might consider:

1. How does compounding frequency affect the APY?
2. What is the difference between nominal interest rate and APY?
3. How would the APY change if the nominal rate were higher?
4. What would be the APY for the same rate if it were compounded annually instead?
5. How do different investment vehicles compare in terms of APY? 

**Tip:** Always consider the compounding frequency when comparing investment options, as it can significantly affect your overall yield.

Find the annual percentage yield for an investment at the following rate. 6.8% compounded monthly.

Discover how to calculate the annual percentage yield (APY) for an investment with a 6.8% nominal interest rate compounded monthly. This guide includes step-by-step calculations and insights on the effects of compounding frequency. Suitable for high school students.

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