An investment pays 8.2% interest, compounded daily, what's the yield?

To calculate the annual yield for an investment that pays 8.2% interest compounded daily, you can use the formula for compound interest yield:

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

Where:
- \( A \) is the final amount
- \( P \) is the principal (initial investment)
- \( r \) is the annual nominal interest rate (in decimal form)
- \( n \) is the number of times interest is compounded per year (for daily compounding, \( n = 365 \))
- \( t \) is the time in years (for yield, we use \( t = 1 \))

The yield \( Y \) is the percentage increase over one year:

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

Let's calculate the yield for an 8.2% interest rate compounded daily.

1. Convert the interest rate to decimal: \( r = \frac{8.2}{100} = 0.082 \).
2. Daily compounding means \( n = 365 \).

Now let's plug these values into the formula:

\[
Y = \left(1 + \frac{0.082}{365}\right)^{365} - 1
\]

I will calculate this next.The yield for an 8.2% interest rate compounded daily is approximately 8.54%.

Would you like further details or explanations?

Here are 5 related questions:
1. How does the yield change with different compounding frequencies?
2. What is the formula for continuous compounding?
3. How do you calculate the yield for an interest compounded quarterly?
4. How is compound interest different from simple interest?
5. What is the effect of increasing the interest rate on the yield?

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

Learn how to calculate the yield for an investment with 8.2% interest compounded daily. This guide covers the compound interest formula, explaining how to find the effective annual yield using daily compounding. Suitable for advanced high school or college-level students.

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