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This question is asking for extra earnings, not total amount.

The question asks: Zoe has $2,000 in an account with a 6.5% APR, compounded daily, and the money will remain there for 3 years. We are to find out how much **extra money** she will earn in interest over the 3 years.

The formula for compound interest is:

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

Where:
- $ A $ is the total amount (principal + interest) after time $ t $,
- $ P $ is the principal amount (initial investment, $2,000),
- $ r $ is the annual interest rate (6.5% = 0.065),
- $ n $ is the number of times interest is compounded per year (since it’s compounded daily, $ n = 365 $),
- $ t $ is the number of years (3 years).

First, let’s calculate the total amount $ A $ after 3 years:

\[
A = 2000 \left(1 + \frac{0.065}{365}\right)^{365 \times 3}
\]

Now, to find the extra earnings (interest), subtract the principal $ P $ from $ A $:

\[
\text{Interest} = A - P
\]

Let me calculate this for you.The total amount Zoe will have after 3 years is approximately **$2,430.58**. The extra money she will earn from interest is about **$430.58**.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How would the interest change if the APR was 7% instead of 6.5%?
2. What if the interest was compounded monthly instead of daily?
3. How much would Zoe earn if she invested the money for 5 years instead of 3?
4. How does compound interest compare with simple interest over the same period?
5. How much should Zoe invest initially to earn $1,000 in interest in 3 years?

**Tip**: The more frequently interest is compounded, the more interest you'll earn due to "interest on interest."

Zoe read an advertisement that offered 6.5% APR on accounts over $2000 left for a minimum of 3 years and compounded daily. She has $2000 and thinks this sounds like a great deal. How much money will she earn in the 3 years?

Learn how to calculate the compound interest earned on an initial investment of $2000 at a 6.5% APR, compounded daily for 3 years. Understand key financial concepts and formulas. Suitable for students in Grades 9-12.

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