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!