The formula for continuous compounding is:

$A = P e^{rt}$

Where:

• $A$ is the amount after time $t$,
• $P$ is the initial principal (starting amount),
• $r$ is the interest rate as a decimal,
• $t$ is the time in years, and
• $e$ is approximately 2.71828.

We are given:

• $P = 400$,
• $r = 0.06$ (since 6% = 0.06),
• $t = 5$ years.

Now, let's calculate the amount $A$:

$A = 400 \times e^{0.06 \times 5}$

I'll compute the result.After 5 years, Franco will have $539.94 in the account.

Would you like more details on this calculation or have any questions?

Here are 5 related questions to consider:

1. How would the amount change if the interest rate was 8% instead of 6%?
2. What if the money was invested for 10 years instead of 5?
3. How does continuous compounding compare to annual compounding in this case?
4. If Franco wanted to have $600 in the account after 5 years, how much should he initially invest?
5. What is the formula for continuous compounding, and how is it derived?

Tip: Continuous compounding generally results in slightly higher amounts compared to periodic compounding.