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Let's break down the problem from your DeltaMath question:

We have two investments:

1. **Nicole's Investment**:
   - Principal: $29,000
   - Interest Rate: 5 ¼ % = 5.25% (as a decimal, 0.0525)
   - Compounded continuously
   - Time: 14 years

   For continuous compounding, we use the formula:
   \[
   A = P \cdot e^{rt}
   \]
   where $A$ is the amount, $P$ is the principal, $r$ is the interest rate, and $t$ is the time in years. $e$ is the base of the natural logarithm (approximately 2.718).

2. **Bentley's Investment**:
   - Principal: $29,000
   - Interest Rate: 4 ⅝ % = 4.625% (as a decimal, 0.04625)
   - Compounded annually
   - Time: 14 years

   For annual compounding, we use the formula:
   \[
   A = P \left(1 + \frac{r}{n}\right)^{nt}
   \]
   where $n = 1$ since it is compounded annually.

Let me calculate how much each person has after 14 years and find the difference.After 14 years:

- Nicole's account grows to approximately **$60,479**.
- Bentley's account grows to approximately **$54,613**.

The difference in favor of Nicole is approximately **$5,866**.

Would you like further details or have any questions?

Here are some related questions for further practice:
1. How would the result change if Bentley’s interest was compounded quarterly instead of annually?
2. What would happen if both accounts were compounded semi-annually?
3. How does continuous compounding differ from annual compounding in general?
4. How would an increase in the investment amount affect the total after 14 years?
5. What would the final amount be for both Nicole and Bentley after 20 years instead of 14?

**Tip:** Continuous compounding typically leads to higher returns compared to annual compounding, especially over longer periods.

Nicole invested $29,000 in an account paying an interest rate of 5 ¼ % compounded continuously. Bentley invested $29,000 in an account paying an interest rate of 4 ⅝ % compounded annually. After 14 years, how much more money would Nicole have in her account than Bentley, to the nearest dollar?

Learn how the difference in compounding methods affects investment growth over 14 years. This problem compares continuous and annual compounding at rates of 5.25% and 4.625% respectively, on an initial investment of $29,000.

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