Use the continuous compound interest formula to find the indicated value.
Pequals=​$3,000​; requals=6.38%; tequals=8 ​years; Aequals=​?
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Part 1
Aequals=​$enter your response here ​

The continuous compound interest formula is given by:

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

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

Given:
- $ P = 3000 $
- $ r = 6.38\% = 0.0638 $
- $ t = 8 $

Now, let's calculate the value of $ A $:

\[
A = 3000 \times e^{0.0638 \times 8}
\]

First, I will calculate $ e^{0.0638 \times 8} $.The amount accumulated after 8 years, including interest, is approximately:

\[
A = 4997.87
\]

Would you like further details or have any questions? Here are five related questions to expand your understanding:

1. How does continuous compounding differ from other types of interest compounding?
2. How would the accumulated amount change if the interest rate was compounded annually instead of continuously?
3. What happens to the final amount if the interest rate increases by 1%?
4. How would you calculate the time required to double your investment with continuous compounding?
5. How does the continuous compound interest formula relate to exponential growth?

**Tip:** Always convert percentages to decimals (by dividing by 100) when using them in formulas.

Use the continuous compound interest formula to find the indicated value. P = $3,000; r = 6.38%; t = 8 years; A = ?

Learn how to use the continuous compound interest formula to calculate the accumulated amount for an investment of $3,000 at an interest rate of 6.38% over 8 years. This example demonstrates exponential growth and key financial concepts. Suitable for Grades 10-12.

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