Find the amount of money accumulated if you invest $10,000 at 3% interest compounded quarterly for 2 years.  Round your answer to the nearest cent.

To calculate the amount of money accumulated, we will use the **compound interest formula**:

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

Where:
- $ A $ is the amount of money accumulated after interest,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (in decimal form),
- $ n $ is the number of times interest is compounded per year,
- $ t $ is the number of years.

Given:
- $ P = 10,000 $,
- $ r = 0.03 $ (3% annual interest),
- $ n = 4 $ (quarterly compounding),
- $ t = 2 $ years.

Now, let's calculate $ A $.

\[
A = 10,000 \left(1 + \frac{0.03}{4}\right)^{4 \times 2}
\]

First, calculate the individual terms:

\[
A = 10,000 \left(1 + \frac{0.03}{4}\right)^{8}
= 10,000 \left(1 + 0.0075\right)^{8}
= 10,000 \left(1.0075\right)^{8}
\]

Now, let's compute the value of $ A $.The accumulated amount of money after 2 years, with an investment of $10,000 at 3% interest compounded quarterly, is approximately **$10,615.99**.

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. How does the frequency of compounding affect the total accumulated amount?
2. What would happen if the interest rate was higher, say 5%?
3. How would the result change if the interest was compounded monthly instead of quarterly?
4. What if the investment duration was 5 years instead of 2?
5. Can the compound interest formula be applied to continuous compounding, and if so, how?

**Tip:** The more frequent the compounding, the greater the accumulated amount will be due to interest being applied on interest more often.

Find the amount of money accumulated if you invest $10,000 at 3% interest compounded quarterly for 2 years. Round your answer to the nearest cent.

Learn how to calculate the compound interest on a $10,000 investment at a 3% annual interest rate, compounded quarterly, for 2 years. Discover how this financial formula helps determine the accumulated amount, including real-world applications in finance. Suitable for high school students in Grades 9-12.

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