Calculate the future value. (Round your answer to two decimal places.)

*P* = $26,000, *r* = 9% compounded monthly, *t* = 7 years

To calculate the future value $ A $ of an investment with monthly compounding, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- $ P = 26,000 $ (the principal),
- $ r = 0.09 $ (annual interest rate as a decimal),
- $ n = 12 $ (compounded monthly, so 12 times per year),
- $ t = 7 $ (time in years).

### Step-by-Step Calculation:

1. **Calculate the monthly interest rate**:
   \[
   \frac{r}{n} = \frac{0.09}{12} = 0.0075
   \]

2. **Calculate the total number of compounding periods**:
   \[
   nt = 12 \times 7 = 84
   \]

3. **Plug values into the formula**:
   \[
   A = 26,000 \left(1 + 0.0075\right)^{84}
   \]

4. **Calculate the expression inside the parentheses**:
   \[
   1 + 0.0075 = 1.0075
   \]

5. **Raise 1.0075 to the power of 84**:
   \[
   1.0075^{84} \approx 1.747422051
   \]

6. **Multiply by the principal**:
   \[
   A \approx 26,000 \times 1.747422051 \approx 45,432.97
   \]

### Final Answer:

\[
A \approx 45,432.97
\]

The future value of the investment is approximately **$45,432.97**.

Would you like more details, or do you have any questions?

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Here are 5 related questions to explore further:
1. What would be the future value if the interest rate increased to 10%?
2. How does changing the compounding frequency to quarterly affect the future value?
3. What is the effective annual rate (EAR) for a 9% nominal rate compounded monthly?
4. How much total interest is earned over the 7 years?
5. How does a change in the investment period, say to 10 years, affect the future value?

**Tip:** Monthly compounding can yield significantly more than annual compounding due to more frequent application of interest.

Calculate the future value. (Round your answer to two decimal places.)

P = $26,000, r = 9% compounded monthly, t = 7 years

Learn to calculate the future value of an investment of $26,000 at a 9% annual interest rate compounded monthly for 7 years. This example covers compound interest principles, exponential growth, and detailed step-by-step calculations. Ideal for high school students in Grades 10-12.

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