Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer to two decimal places.)

*P* = $3600, *r* = 4% compounded monthly, *t* = 10 years

To calculate the compound amount, we use the **compound amount formula**:

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

Where:
- $A$ is the compound amount (the value of the investment after interest),
- $P$ is the principal amount ($3600),
- $r$ is the annual interest rate (4% or 0.04),
- $n$ is the number of times the interest is compounded per year (monthly compounding, so $n = 12$),
- $t$ is the time the money is invested or borrowed for (10 years).

### Substituting the given values into the formula:

\[
A = 3600 \left( 1 + \frac{0.04}{12} \right)^{12 \times 10}
\]

\[
A = 3600 \left( 1 + 0.0033333 \right)^{120}
\]

\[
A = 3600 \left( 1.0033333 \right)^{120}
\]

Now, calculate $1.0033333^{120}$ and then multiply by 3600.

\[
A \approx 3600 \times 1.488864
\]

\[
A \approx 5360.31
\]

### The compound amount is approximately **$5360.31**.

Would you like more details, or have any questions?

Here are 5 related questions:
1. How does changing the interest rate affect the compound amount?
2. What happens if the interest is compounded quarterly instead of monthly?
3. How would the calculation change if the investment period were reduced to 5 years?
4. How do you calculate continuous compounding?
5. What is the difference between simple and compound interest?

**Tip:** The more frequently interest is compounded, the higher the final amount will be.

Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer to two decimal places.) *P* = $3600, *r* = 4% compounded monthly, *t* = 10 years

Learn how to calculate the compound interest for an investment of $3600 at an annual interest rate of 4%, compounded monthly for 10 years. This detailed guide covers exponential growth and the compound interest formula, suitable for students in Grades 10-12.

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