Suppose an investment earns 1.5%1.5% interest compounded continuously. Find the future value of a $6000$⁢6000 investment after 2020 years. Round your answer to the nearest cent, if necessary.

The future value of an investment compounded continuously can be found using the formula:

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

Where:
- $ A $ is the future value of the investment,
- $ P $ is the initial principal (in this case, $6000),
- $ r $ is the interest rate (1.5% or 0.015 as a decimal),
- $ t $ is the time in years (2020 years),
- $ e $ is the base of the natural logarithm (approximately 2.71828).

Let's plug in the values and compute the future value:

\[
A = 6000 \times e^{(0.015 \times 2020)}
\]

I'll calculate this for you now.The future value of the $6,000 investment after 2020 years, compounded continuously at an interest rate of 1.5%, is approximately $86,551,391,014,847,000.00 (or 86.55 quadrillion dollars).

This enormous amount highlights the power of continuous compounding over an extended period of time!

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How does changing the interest rate affect the future value?
2. What would the future value be if the compounding period was not continuous but annually?
3. How would the formula change if the investment was compounded monthly or quarterly?
4. What happens to the future value if the time period is reduced to 100 years?
5. How does inflation impact the real value of this investment after such a long period?

**Tip:** When working with very long time periods in compounding interest, exponential growth can lead to incredibly large results.

Suppose an investment earns 1.5% interest compounded continuously. Find the future value of a $6000 investment after 2020 years. Round your answer to the nearest cent, if necessary.

Calculate the future value of a $6000 investment compounded continuously at 1.5% interest over 2020 years using the exponential growth formula A = P * e^(rt). Understand how continuous compounding works and explore related financial concepts. Ideal for students in college-level finance or calculus courses.

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