Amanda invests $5400 in a new savings account which earns 5.8% annual interest, compounded continuously.  What will be the value of her investment after 5 years?  Round to the nearest cent.

The formula for continuous compounding is given by:

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

Where:
- $ A $ is the amount of money accumulated after time $ t $ (the future value),
- $ 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).

For Amanda's investment:
- $ P = 5400 $,
- $ r = 5.8\% = 0.058 $,
- $ t = 5 $.

Now, we substitute these values into the formula:

\[
A = 5400 \times e^{0.058 \times 5}
\]

Let me calculate that for you.The value of Amanda's investment after 5 years, with continuous compounding at an annual interest rate of 5.8%, will be **$7216.71**.

Do you want more details or have any questions? Here are 5 related questions to expand on the concept:

1. How does the result change if the interest is compounded annually instead of continuously?
2. What happens if Amanda invests the money for 10 years instead of 5?
3. How would the future value change if the interest rate increased to 7%?
4. What is the difference between simple interest and compound interest?
5. How can you calculate the doubling time for an investment with continuous compounding?

**Tip**: Continuous compounding leads to slightly higher returns compared to standard compounding at regular intervals like yearly or monthly.

Amanda invests $5400 in a new savings account which earns 5.8% annual interest, compounded continuously. What will be the value of her investment after 5 years? Round to the nearest cent.

Learn how Amanda's $5400 investment grows to $7216.71 in 5 years with continuous compounding at 5.8% interest. This problem explores exponential growth, continuous compounding, and future value calculations, suitable for high school students in Grades 10-12.

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