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To solve this problem, which involves continuous compounding interest, we can use the formula:

\[
A = P \cdot e^{(r \cdot t)}
\]

where:
- $ A $ is the amount of money in the account after $ t $ years.
- $ P $ is the principal amount (initial deposit), which is $6000 in this case.
- $ r $ is the interest rate (5%, or 0.05 as a decimal).
- $ t $ is the time in years (5 years here).
- $ e $ is the mathematical constant, approximately equal to 2.71828.

### Step-by-Step Solution:
1. **Identify the values:**
   - $ P = 6000 $
   - $ r = 0.05 $
   - $ t = 5 $

2. **Substitute these values into the formula:**
   \[
   A = 6000 \cdot e^{(0.05 \cdot 5)}
   \]

3. **Calculate the exponent:**
   \[
   0.05 \times 5 = 0.25
   \]

4. **Rewrite the equation:**
   \[
   A = 6000 \cdot e^{0.25}
   \]

5. **Calculate $ e^{0.25} $:**
   \[
   e^{0.25} \approx 1.2840
   \]

6. **Multiply by the principal amount:**
   \[
   A \approx 6000 \cdot 1.2840 = 7704
   \]

So, the amount in the account after 5 years will be approximately **$7704**.

Would you like further details on any steps?

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Here are some related questions to further explore:

1. How would the result change if the interest rate were 6% instead of 5%?
2. What would the balance be if the interest were compounded annually instead of continuously?
3. How long would it take for the amount to double with a 5% interest rate compounded continuously?
4. What is the difference between continuous compounding and discrete compounding?
5. Can you derive the continuous compounding formula from first principles?

**Tip:** When dealing with continuous compounding, the base of the exponential function is always $ e $, the natural constant, which simplifies calculations for continuous growth scenarios.

You deposit $6000 in an account earning 5% interest compounded continuously. How much will you have in the account in 5 years?

Learn how to calculate the future value of a $6000 investment with a 5% interest rate compounded continuously over 5 years. This example demonstrates the continuous compounding formula and exponential growth. Suitable for high school students studying exponential functions.

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