Suppose that you invest $25,000 in an account that earns interest at an APR of 1.8%, compounded continuously. Determine the accumulated balance after 7 years.



 $29,221.51


 $28,386.14


 $28,357.05


 $28,350.54


 None of the above.

To determine the accumulated balance after 7 years in an account with continuous compounding, we use the formula for continuous compound interest:

\[
A = P e^{rt}
\]

Where:
- $A$ is the accumulated balance,
- $P = 25,000$ (the initial investment),
- $r = 0.018$ (the annual interest rate of 1.8%),
- $t = 7$ years,
- $e$ is Euler's number (approximately 2.71828).

Now, let's calculate $A$:

\[
A = 25,000 \times e^{(0.018 \times 7)}
\]

I'll compute this value.

The accumulated balance after 7 years is approximately \$28,357.05. 

Thus, the correct answer is **$28,357.05**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the balance change if the interest rate were higher, say 2.5%?
2. What happens to the accumulated balance if the investment period is extended to 10 years?
3. How does continuous compounding differ from annual or monthly compounding?
4. How can you determine the time it will take for the investment to double with continuous compounding?
5. What is Euler's number, and why is it used in continuous compounding?

**Tip:** Continuous compounding leads to the fastest growth for an investment compared to other compounding intervals.

Suppose that you invest $25,000 in an account that earns interest at an APR of 1.8%, compounded continuously. Determine the accumulated balance after 7 years.

Determine the accumulated balance of a $25,000 investment after 7 years with a continuous compounding interest rate of 1.8% APR. Using the formula A = P e^(rt), this problem explores exponential growth and continuous compound interest. Suitable for Grades 10-12.

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