Find the amount A in dollars of $8,000 invested for 30 years at 9% compounded continuously. (Enter a number. Round answer to the nearest cent.)
$

To find the future amount $ A $ of an investment compounded continuously, we use the formula for continuous compounding:

\[
A = P e^{rt}
\]

Where:
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time the money is invested for (in years),
- $ e $ is Euler's number (approximately 2.71828).

Given:
- $ P = 8000 $ dollars,
- $ r = 9\% = 0.09 $,
- $ t = 30 $ years.

Now, let's compute the amount $ A $:

\[
A = 8000 \times e^{(0.09 \times 30)}
\]

I'll calculate this value.The amount $ A $ after 30 years of continuous compounding at 9% interest is **$119,037.85**.

Do you have any further questions or would you like a detailed explanation of the steps?

Here are five related questions to consider:
1. What would the amount be if the interest rate were 10% instead of 9%?
2. How would the total change if the investment period were 40 years?
3. What is the formula for compounding interest monthly or annually instead of continuously?
4. How does continuous compounding differ from other types of compounding?
5. What would be the effect on the amount if the initial investment was $10,000 instead of $8,000?

**Tip:** Continuous compounding grows faster than other compounding methods because it calculates interest at an infinitely small interval.

Find the amount A in dollars of $8,000 invested for 30 years at 9% compounded continuously. (Enter a number. Round answer to the nearest cent.)

Learn how to calculate the future value of an $8,000 investment compounded continuously at a 9% interest rate for 30 years. This problem demonstrates the use of the continuous compounding formula A = P e^{rt}, resulting in a future value of $119,037.85. Ideal for students in Grades 11-12.

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