Suppose that you invest $23,000 in an account that earns interest at an APR of 1.5%, compounded continuously. Determine the accumulated balance after 9 years.



 $26,379.07


 $25,972.11


 $26,331.78


 $26,324.35


 None of the above.


To determine the accumulated balance after 9 years with continuous compounding, we can use the formula for continuous compound interest:

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

Where:
- $A$ is the accumulated balance.
- $P$ is the initial principal ($23,000).
- $r$ is the annual interest rate (1.5% or 0.015).
- $t$ is the time in years (9 years).
- $e$ is the base of the natural logarithm (approximately 2.71828).

Substituting the values into the formula:

\[
A = 23000 \times e^{0.015 \times 9}
\]

Now let's calculate this.

The accumulated balance after 9 years is approximately **$26,324.35**, which matches one of the options provided.

Do you have any questions or need further details?

Here are 5 related questions for further exploration:
1. How would the accumulated balance change if the APR was 2% instead of 1.5%?
2. What is the difference between simple interest and continuously compounded interest?
3. How does the frequency of compounding affect the final amount?
4. How long would it take to double the investment at 1.5% APR with continuous compounding?
5. What happens to the formula if the interest is compounded quarterly instead of continuously?

**Tip:** Continuous compounding provides slightly higher returns compared to regular compounding at finite intervals.

Suppose that you invest $23,000 in an account that earns interest at an APR of 1.5%, compounded continuously. Determine the accumulated balance after 9 years.

Calculate the accumulated balance of a $23,000 investment at an APR of 1.5%, compounded continuously over 9 years. Using the formula A = P * e^(rt), find that the final amount is approximately $26,324.35. Suitable for advanced high school students in Grades 11-12.

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