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Part 1
If ​$4 comma 0004,000 is invested at 44​% compounded quarterlyquarterly​, what is the amount after 44 ​years?
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Part 1
The amount after 44 years will be ​$enter your response here.

To solve this problem, we need to use the formula for compound interest:

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

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

Given:
- $ P = 4,000 $,
- $ r = 0.44 $ (44% interest rate),
- $ n = 4 $ (since it's compounded quarterly),
- $ t = 44 $ years.

Now, substitute the values into the formula:

\[
A = 4,000 \left( 1 + \frac{0.44}{4} \right)^{4 \times 44}
\]

First, simplify the expression inside the parentheses:

\[
A = 4,000 \left( 1 + 0.11 \right)^{176} = 4,000 \times (1.11)^{176}
\]

Next, calculate $ (1.11)^{176} $ and then multiply by 4,000.

Let's compute that:

\[
A = 4,000 \times (1.11)^{176}
\]

After calculation, $ (1.11)^{176} \approx 7287.49 $, so:

\[
A \approx 4,000 \times 7287.49 = 29,149,960
\]

Thus, the amount after 44 years will be approximately **$29,149,960**.

Would you like more details on how this was calculated or any specific questions?

Here are 5 related questions:
1. What happens if the interest is compounded monthly instead of quarterly?
2. How would the total amount change if the investment period is shortened to 30 years?
3. What would be the effect if the interest rate was 50% instead of 44%?
4. How does the frequency of compounding impact the final amount?
5. What is the formula for continuous compounding and how would it apply here?

**Tip:** Compound interest grows exponentially, meaning the longer you invest, the greater the growth, especially with higher interest rates and more frequent compounding.

If $4,000 is invested at 44% compounded quarterly, what is the amount after 44 years?

Learn how to calculate the compound interest for an investment of $4,000 at an interest rate of 44% compounded quarterly over a period of 44 years. This step-by-step solution explains key concepts such as the compound interest formula and exponential growth, suitable for Grades 10-12.

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