For continuous compounding, the amount of money in the account after a certain period can be calculated using the formula:

$A = P \times e^{rt}$

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $t$ is the time the money is invested for, in years.
• $e$ is the base of the natural logarithm, approximately equal to 2.71828.

Given:

• $P = 3,100$
• $r = 3.6\% = 0.036$
• $t = 19$ years

Now, let's calculate the final amount using the formula.After 19 years, Juan would have approximately $6,144 in the account, rounded to the nearest dollar.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How much would Juan have if the interest rate was 5% instead of 3.6%?
2. What would be the amount if the investment period was 25 years instead of 19 years?
3. How does the final amount compare with daily compounding instead of continuous compounding at the same rate?
4. What is the difference in the final amount if Juan invested $5,000 instead of $3,100?
5. How long would it take for Juan's investment to double with continuous compounding at 3.6%?

Tip: Continuous compounding leads to a slightly higher amount compared to daily or monthly compounding, especially over longer periods.