To determine how much you'll have in the account in 5 years with continuous compounding interest, we use the formula:

$A = P e^{rt}$

where:

• $A$ is the amount in the account after time $t$,
• $P$ is the principal (initial deposit),
• $r$ is the interest rate,
• $t$ is the time in years, and
• $e$ is the base of the natural logarithm (approximately 2.71828).

For this problem:

• $P = 2000$,
• $r = 0.05$,
• $t = 5$.

Substituting these values into the formula:

$A = 2000 \times e^{0.05 \times 5}$

Calculating this:

1. First, find $0.05 \times 5 = 0.25$.
2. Then, calculate $e^{0.25} \approx 1.2840$.
3. Multiply by the principal: $2000 \times 1.2840 = 2568.08$.

So, the amount in the account after 5 years will be approximately $2568.08.

Would you like more details or have any questions?

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Here are some additional questions related to this topic:

1. How would the amount change if the interest rate was 6% instead of 5%?
2. What if the deposit period was 10 years instead of 5 years?
3. How much interest would be earned if the interest were compounded annually instead?
4. What is the difference between continuous compounding and monthly compounding?
5. How does changing the initial deposit amount affect the final balance?

Tip: Continuous compounding yields a slightly higher amount than periodic compounding, especially as the interest rate or time increases.