Find the amount A accumulated after investing a principal Pequals​$11 comma 000 for tequals10 years at an interest rate requals3​% compounded quarterly. ​(Assume no withdrawals are​ made.)
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Question content area right
Part 1
The amount after 10 years will be
​$
  
enter your response here.
​(Round to the nearest​ cent.)

To find the accumulated amount $ A $ after 10 years with compound interest, we use the formula:

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

where:
- $ P = 11,000 $ (the principal),
- $ r = 0.03 $ (annual interest rate in decimal form),
- $ t = 10 $ years (time),
- $ n = 4 $ (number of times interest is compounded per year, since it's compounded quarterly).

### Step-by-step:

1. **Substitute the values into the formula**:
\[
A = 11,000 \left( 1 + \frac{0.03}{4} \right)^{4 \times 10}
\]

2. **Simplify the expression**:
\[
A = 11,000 \left( 1 + 0.0075 \right)^{40}
\]
\[
A = 11,000 \left( 1.0075 \right)^{40}
\]

Now, we can calculate the value of $ (1.0075)^{40} $ and then multiply by 11,000 to find $ A $.

Let me compute that for you.The accumulated amount after 10 years is approximately **$14,831.83**.

Would you like any more details on this, or have any further questions?

Here are five related questions to explore:

1. How does increasing the interest rate affect the final accumulated amount?
2. What happens if the interest is compounded monthly instead of quarterly?
3. How much interest is earned after 10 years?
4. What would the accumulated amount be if the investment period were 15 years instead of 10?
5. How would the result change if withdrawals were allowed during the investment period?

**Tip:** Compounding more frequently (e.g., monthly vs. quarterly) generally results in a higher accumulated amount because interest is applied more often.

Find the amount A accumulated after investing a principal P = $11,000 for t = 10 years at an interest rate r = 3% compounded quarterly. Assume no withdrawals are made. What is the amount after 10 years? (Round to the nearest cent.)

Learn how to calculate the accumulated amount after investing $11,000 for 10 years at an interest rate of 3% compounded quarterly. This problem covers key concepts such as compound interest and exponential growth, using the formula A = P(1 + r/n)^(nt). Perfect for students in Grades 10-12.

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