An investment of $25,000 earns 2.35% annual interest and is compounded continuously. If no funds are added or removed from this account, what is the future value of the investment after 5 years? 

Round your answer to the nearest penny.

To calculate the future value of an investment compounded continuously, we use the formula:

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

Where:
- $A$ is the future value of the investment,
- $P$ is the initial principal (investment amount),
- $r$ is the annual interest rate (as a decimal),
- $t$ is the time the money is invested for (in years),
- $e$ is the mathematical constant (approximately 2.71828).

In this case:
- $P = 25,000$,
- $r = 2.35\% = 0.0235$,
- $t = 5$ years.

Now, let's calculate the future value.

\[
A = 25,000 \cdot e^{0.0235 \cdot 5}
\]The future value of the investment after 5 years, with continuous compounding, is approximately **$28,117.04**.

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:
1. How would the future value change if the interest rate increased to 3%?
2. What if the investment period was extended to 10 years?
3. How does continuous compounding differ from annual compounding?
4. What is the formula for compound interest when compounded quarterly?
5. How can we calculate the time needed to double the investment?

**Tip:** Continuous compounding results in slightly higher returns compared to other compounding methods due to the constant application of interest.

An investment of $25,000 earns 2.35% annual interest and is compounded continuously. If no funds are added or removed from this account, what is the future value of the investment after 5 years? Round your answer to the nearest penny.

Calculate the future value of a $25,000 investment with a 2.35% annual interest rate compounded continuously over 5 years. Using the formula A = P * e^(rt), discover how continuous compounding affects investment growth. Suitable for students in Grades 11-12.

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