Use the compound interest formula to determine the accumulated balance after the stated period.
​$3000 invested at an APR of 9​% for 10 years.
If interest is compounded​ annually, what is the amount of money after 10 ​years?
Do not round until the final answer. Then round to the nearest cent as​ needed.)

To determine the accumulated balance using the compound interest formula, we use the following formula:

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

Where:
- $A$ is the amount of money after interest (the accumulated balance),
- $P$ is the principal amount (initial investment),
- $r$ is the annual interest rate (as a decimal),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the number of years the money is invested or borrowed for.

Given:
- $P = 3000$ (initial investment),
- $r = 9\% = 0.09$ (APR as a decimal),
- $n = 1$ (since interest is compounded annually),
- $t = 10$ years.

Substitute these values into the formula:

\[
A = 3000 \left(1 + \frac{0.09}{1}\right)^{1 \times 10}
\]
\[
A = 3000 \left(1 + 0.09\right)^{10}
\]
\[
A = 3000 \times (1.09)^{10}
\]

Now let's calculate the value of $A$.The accumulated balance after 10 years, with a $3000 investment at an APR of 9% compounded annually, is approximately **$7102.09**.

Do you want more details or have any further questions? 

Here are 5 related questions:
1. What happens if the interest is compounded monthly instead of annually?
2. How does the investment grow if the APR is increased to 12%?
3. What would the accumulated balance be after 15 years instead of 10?
4. How does simple interest compare to compound interest in this case?
5. What is the formula for continuous compound interest, and how would it apply here?

**Tip:** The more frequently interest is compounded, the greater the accumulated balance will be over time.

Use the compound interest formula to determine the accumulated balance after the stated period. $3000 invested at an APR of 9​% for 10 years. If interest is compounded​ annually, what is the amount of money after 10 ​years? Do not round until the final answer. Then round to the nearest cent as​ needed.

Find out how to calculate the accumulated balance of $3000 invested at 9% APR for 10 years, with interest compounded annually. This problem involves the compound interest formula and explores exponential growth in financial mathematics. Suitable for high school students and above.

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