An investor has $16,000 to invest and is willing to keep it invested for up to five years. A savings account offers 1.57% 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= é 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 calculate the future value of an investment compounded continuously, we use the following formula:

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

Where:
- $ A $ is the future value,
- $ P $ is the initial principal (the amount invested),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time in years, and
- $ e $ is Euler's number (approximately 2.71828).

### Given:
- $ P = 16,000 $ (the amount invested),
- $ r = 1.57\% = 0.0157 $,
- $ t = 5 $ years.

Substituting the values into the formula:

\[
A = 16,000 \cdot e^{0.0157 \cdot 5}
\]

Now I'll calculate the future value.The future value of the investment, after 5 years with continuous compounding at an interest rate of 1.57%, is approximately **$17,306.61**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How does continuous compounding differ from annual or quarterly compounding?
2. What is the effect of a higher interest rate on the future value?
3. How would the future value change if the investment was kept for 10 years instead of 5?
4. How do you calculate the effective annual rate for continuous compounding?
5. What are some other financial products that use continuous compounding?

**Tip:** Continuous compounding maximizes the return on an investment by compounding at an infinite number of intervals within a year!

An investor has $16,000 to invest and is willing to keep it invested for up to five years. A savings account offers 1.57% interest compounded continuously. What is the future value of the investment?

Learn how to calculate the future value of a $16,000 investment compounded continuously at an interest rate of 1.57% for 5 years. The problem covers exponential growth concepts using the continuous compound interest formula. Suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation