An investor has $14,000 to invest and is willing to keep it invested for up to five years. A savings account offers 1.62% interest compounded continuously.
You can remove the money any time you like, but plan to keep it in the investment for 5 years.
(For interest compounded continuously, the effective rate formula is E= e' r-1.) Do not round intermediate calculation
Part 1 of 2
What is the future value of the investment? Round to the nearest cent.
The future value for this investment is $_

To find the future value of an investment with continuous compounding interest, we can use the formula:

\[
A = P \cdot e^{r \cdot t}
\]

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

Given:
- $ P = 14,000 $ (initial investment),
- $ r = 1.62\% = 0.0162 $ (interest rate as a decimal),
- $ t = 5 $ years.

We will now calculate the future value $ A $.

\[
A = 14000 \cdot e^{0.0162 \cdot 5}
\]

Let me calculate that.The future value of the investment after 5 years, with continuous compounding at an interest rate of 1.62%, is approximately **$15,181.19**.

Would you like more details on how this is calculated, or do you have any other questions?

Here are 5 related questions to consider:
1. How would the future value change if the interest rate were higher?
2. What happens to the future value if the investment period is increased?
3. How does continuous compounding differ from annual compounding?
4. What is the total interest earned over the 5 years?
5. How would monthly contributions affect the future value?

**Tip:** Continuous compounding tends to yield slightly higher returns compared to other compounding methods, especially over long periods.

An investor has $14,000 to invest and is willing to keep it invested for up to five years. A savings account offers 1.62% interest compounded continuously. You can remove the money any time you like, but plan to keep it in the investment for 5 years. What is the future value of the investment? Round to the nearest cent.

Find out how to calculate the future value of a $14,000 investment with a 1.62% interest rate compounded continuously over 5 years. Learn about continuous compounding, exponential growth, and the formula used to determine the future value of the investment, yielding approximately $15,181.19.

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