Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer to two decimal places.)
P = $6200, r = 3% compounded monthly, t = 10 years

To find the compound amount, we use the formula:

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

where:
- $ A $ is the compound amount (what we are solving for),
- $ P $ is the principal (initial amount), which is $6200,
- $ r $ is the annual interest rate, which is 3% or 0.03,
- $ n $ is the number of times interest is compounded per year (monthly compounding means $ n = 12 $),
- $ t $ is the time in years, which is 10.

### Step-by-Step Solution

1. **Substitute values into the formula:**

   \[
   A = 6200 \left(1 + \frac{0.03}{12}\right)^{12 \cdot 10}
   \]

2. **Calculate the monthly interest rate**:

   \[
   \frac{0.03}{12} = 0.0025
   \]

   So, the formula becomes:

   \[
   A = 6200 \left(1 + 0.0025\right)^{120}
   \]

3. **Calculate the expression inside the parentheses**:

   \[
   1 + 0.0025 = 1.0025
   \]

4. **Raise $ 1.0025 $ to the power of 120**:

   \[
   1.0025^{120} \approx 1.34935
   \]

5. **Multiply by the principal**:

   \[
   A = 6200 \times 1.34935 \approx 8365.97
   \]

### Final Answer

The compound amount $ A $ after 10 years is approximately:

\[
\boxed{8365.97}
\]

Would you like more details or have any questions?

Here are related questions:
1. How does the frequency of compounding impact the final amount?
2. What is the difference between simple and compound interest?
3. How would the amount change if the interest rate increased to 4%?
4. What would happen if the interest were compounded quarterly instead of monthly?
5. How can this formula be adapted for continuous compounding?

**Tip:** Increasing compounding frequency increases the final amount due to more frequent application of interest.

Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer to two decimal places.) P = $6200, r = 3% compounded monthly, t = 10 years

Learn how to calculate the compound amount for a principal of $6200 invested at a 3% interest rate, compounded monthly over 10 years. This guide provides a step-by-step solution using the compound interest formula, ideal for high school math students.

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