To find the amount of money in the investment account after 19 years, we can use the formula for continuous compounding:

$V = P \cdot e^{rt}$

where:

• $V$ is the value of the account after $t$ years,
• $P$ is the initial principal ($98,800),
• $r$ is the annual interest rate (4% or 0.04),
• $t$ is the time in years (19 years),
• $e$ is the base of the natural logarithm (approximately 2.71828).

Now, plug in the values:

$V = 98,800 \cdot e^{0.04 \times 19}$

Let's calculate this step by step.

First, calculate the exponent:

$0.04 \times 19 = 0.76$

Next, calculate $e^{0.76}$:

$e^{0.76} \approx 2.138$

Finally, multiply this by the principal:

$V \approx 98,800 \cdot 2.138 \approx 211,014.40$

So, the value of the account after 19 years is approximately $211,014.40.

Would you like further details or have any questions? Here are some related questions:

1. How does the compounding frequency affect the final amount in an investment account?
2. What is the difference between continuous compounding and annual compounding?
3. How would the final amount change if the interest rate were 5% instead of 4%?
4. What happens to the value of the investment if the time period is increased to 25 years?
5. Can you derive the formula $V = P \cdot e^{rt}$ from the basic interest formulas?

Tip: Continuous compounding results in the highest possible returns because it effectively compounds an infinite number of times per year.