if i have earned $8270 in interest with a principal of $39844 over 10 years, what is my average annual interest rate?

To find the average annual interest rate, we can use the formula for simple interest:

\[
I = P \times r \times t
\]

Where:
- $ I $ is the interest earned ($8,270),
- $ P $ is the principal amount ($39,844),
- $ r $ is the annual interest rate (which we need to find), and
- $ t $ is the time in years (10 years).

Rearranging the formula to solve for the interest rate $ r $:

\[
r = \frac{I}{P \times t}
\]

Substituting the given values:

\[
r = \frac{8270}{39844 \times 10}
\]

Now, let's calculate it:

\[
r = \frac{8270}{398440} \approx 0.02075
\]

So the average annual interest rate $ r $ is approximately 0.02075, or **2.075%**.

Would you like further details or have any questions?

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Here are some related questions you might find interesting:

1. What would the interest earned be if the interest rate was compounded annually instead of being simple?
2. How much would the principal grow to if it was invested for 15 years instead of 10?
3. What is the difference between simple and compound interest?
4. How do you calculate the interest rate if you have compounded interest?
5. What would be the interest earned with a higher principal, say $50,000, under the same conditions?
6. How would the interest change if the annual interest rate was 3% instead of what you calculated?
7. Can you derive the formula for calculating interest for varying interest rates over the years?
8. How do taxes affect the interest earned on an investment?

**Tip:** Always keep track of whether the interest rate is simple or compounded, as this significantly impacts the final amount.

Learn how to calculate the average annual interest rate using the simple interest formula. Given a principal of $39,844 and an interest earned of $8,270 over 10 years, find the annual interest rate. Detailed step-by-step solution provided.

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