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

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

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

where:
- $ A $ is the future value of the investment,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time 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 in decimal form),
- $ t = 5 $ years.

Let's calculate the future value.The future value of the investment, after 5 years, is approximately **$15,181.19**.

Would you like more details or have any other questions?

Here are five related questions you might find useful:
1. What happens if the interest rate changes to 2%?
2. How much would the investor have after 3 years instead of 5?
3. How does continuous compounding compare to annual compounding in this scenario?
4. How much interest is earned after 5 years?
5. What is the effective annual rate for this investment?

**Tip:** Continuous compounding grows faster than compounding at regular intervals because interest is added to the principal continuously.

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.

Calculate the future value of an investment of $14,000 with 1.62% interest compounded continuously for 5 years. Learn how to apply the continuous compounding formula A = P * e^(rt) to find the future value of this investment, resulting in approximately $15,181.19.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation