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 calculate the compound amount $ A $ with interest compounded monthly, we use the formula:

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

where:
- $ P = 6200 $ (initial principal),
- $ r = 0.03 $ (annual interest rate as a decimal),
- $ n = 12 $ (number of times compounded per year, since it's monthly),
- $ t = 10 $ (time in years).

### Step-by-Step Calculation:

1. **Convert the interest rate per compounding period**:
   \[
   \frac{r}{n} = \frac{0.03}{12} = 0.0025
   \]

2. **Calculate the total number of compounding periods**:
   \[
   n \cdot t = 12 \cdot 10 = 120
   \]

3. **Plug into the compound interest formula**:
   \[
   A = 6200 \times \left(1 + 0.0025\right)^{120}
   \]
   \[
   A = 6200 \times \left(1.0025\right)^{120}
   \]

4. **Calculate the exponent**:
   \[
   A \approx 6200 \times 1.34935
   \]

5. **Final result**:
   \[
   A \approx 8376.97
   \]

### Answer:
The compound amount after 10 years is approximately **$8376.97**.

Would you like more details, or have any questions?

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**Related Questions:**
1. How would the result change if compounded quarterly instead of monthly?
2. What would the compound amount be if the rate were 4% instead of 3%?
3. How does continuous compounding compare to monthly compounding?
4. What is the difference between simple and compound interest for this scenario?
5. How would the formula change if compounded daily?

**Tip:** When calculating compound interest, double-check the compounding frequency, as it affects the final amount significantly.

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

Calculate the compound amount for an initial principal of $6200 with an interest rate of 3% compounded monthly over 10 years. This solution uses the compound interest formula and provides a detailed, step-by-step calculation, rounding the final answer to two decimal places. Ideal for students in Grades 10-12.

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