You invest $13,000 at 6% interest, compounded monthly, for 2 years. Use the compound interest formula to calculate the compound amount (in $) for your investment. (Round your answer to the nearest cent.)
$

The compound interest formula is:

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

Where:
- $A$ is the compound amount (future value).
- $P$ is the principal (initial investment), which is $13,000.
- $r$ is the annual interest rate (6%, or 0.06 as a decimal).
- $n$ is the number of times the interest is compounded per year (monthly, so $n = 12$).
- $t$ is the time in years (2 years).

Now, substitute the values into the formula:

\[
A = 13,000 \left(1 + \frac{0.06}{12}\right)^{12 \times 2}
\]

Let me calculate that.The compound amount after 2 years is approximately **$14,653.08**.

Do you want more details or have any questions?

Here are 5 related questions to explore:
1. What would the compound amount be if the interest rate was 5% instead of 6%?
2. How does increasing the compounding frequency (e.g., daily) affect the final amount?
3. What would the total interest earned be after 2 years?
4. How does the investment change if compounded annually instead of monthly?
5. What happens if you invest for 5 years instead of 2?

**Tip:** The more frequently interest is compounded, the greater the future value will be.

You invest $13,000 at 6% interest, compounded monthly, for 2 years. Use the compound interest formula to calculate the compound amount (in $) for your investment. (Round your answer to the nearest cent.)

Learn how to calculate the compound amount for an investment of $13,000 at 6% interest, compounded monthly, for 2 years. This detailed step-by-step solution uses the compound interest formula and is suitable for high school students in Grades 9-12. Final amount: $14,653.08.

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