Use the compound interest formula to find the future value A for the following values.
Upper P equals $ 1 comma 500
i equals 0.052
n equals 23
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Part 1
Upper A equals $
  
enter your response here ​(Round to the nearest​ cent.)


The compound interest formula is:

\[
A = P \left(1 + i\right)^n
\]

Where:
- $ A $ is the future value
- $ P = 1,500 $ is the principal amount
- $ i = 0.052 $ is the interest rate per period
- $ n = 23 $ is the number of periods

Now, substituting the given values into the formula:

\[
A = 1500 \left(1 + 0.052\right)^{23}
\]
\[
A = 1500 \left(1.052\right)^{23}
\]

Let me calculate this for you.

The future value $ A $ after 23 periods is approximately \$4,813.41 when rounded to the nearest cent.

Would you like further details or have any questions?

Here are some related questions to consider:
1. How does increasing the interest rate affect the future value?
2. What happens if the number of periods $ n $ is doubled?
3. How would different compounding frequencies (e.g., quarterly, monthly) impact the result?
4. What is the difference between simple and compound interest in this context?
5. How would reducing the principal $ P $ to \$1,000 change the future value?

**Tip:** Increasing the compounding frequency (monthly, quarterly, etc.) for a fixed interest rate will generally increase the future value.

Use the compound interest formula to find the future value A for the following values. P = $1,500, i = 0.052, n = 23. A = ? (Round to the nearest cent.)

Learn how to calculate the future value using the compound interest formula for P = $1,500, an interest rate of 5.2%, and a period of 23 years. This example demonstrates key concepts in exponential growth and finance, suitable for high school students in Grades 9-12.

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