The formula for continuous compound interest is:

$A = P e^{rt}$

Where:

• $A$ is the future value.
• $P$ is the principal (initial investment), which is $5200.
• $r$ is the annual interest rate (1.3% or 0.013 as a decimal).
• $t$ is the time in years (17 years).
• $e$ is the base of the natural logarithm (approximately 2.71828).

Now, let's plug the values into the formula:

$A = 5200 \cdot e^{(0.013 \cdot 17)}$

First, calculate the exponent:

$0.013 \cdot 17 = 0.221$

Then:

$A = 5200 \cdot e^{0.221}$

Using the value of $e^{0.221} \approx 1.247$:

$A \approx 5200 \cdot 1.247 \approx 6474.40$

So, the future value of the investment is approximately $6474.40.

Would you like more details on how this was calculated, or is there something else you’d like to explore?

Here are 5 related questions you might find interesting:

1. How does continuous compounding compare to other types of compounding (like annual or quarterly)?
2. How would the future value change if the interest rate was 3% instead of 1.3%?
3. What would the future value be if the investment was only made for 10 years instead of 17?
4. How can you calculate the effective interest rate for continuously compounded interest?
5. What other factors can affect the future value of an investment besides the interest rate and time?

Tip: If you're ever unsure of the formula, remember that continuous compounding uses the exponential function $e$, which is unique to this type of interest!