Manually calculate the compound amount and compound interest (in $) for the investment.
Principal	Time
Period (years)	Nominal
Rate (%)	Interest
Compounded	Compound
Amount	Compound
Interest
$3,000	2	10	annually	$  	$

To manually calculate the **compound amount** and **compound interest** for an investment, we'll use the **compound interest formula**:

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

Where:
- $A$ = future value (compound amount)
- $P$ = principal amount ($3,000)
- $r$ = nominal annual interest rate (10% = 0.10)
- $t$ = time the money is invested for (2 years)
- $n$ = number of times the interest is compounded per year (since it's compounded annually, $n = 1$)

### Step 1: Calculate the Compound Amount (A)

Using the formula:

\[
A = 3000 \left(1 + \frac{0.10}{1}\right)^{1 \times 2}
\]

Simplify:

\[
A = 3000 \left(1 + 0.10\right)^{2} = 3000 \times (1.10)^2
\]

Now calculate $1.10^2$:

\[
A = 3000 \times 1.21 = 3,630
\]

Thus, the **compound amount** is **$3,630**.

### Step 2: Calculate the Compound Interest

Compound interest is the difference between the compound amount and the initial principal:

\[
\text{Compound Interest} = A - P = 3,630 - 3,000 = 630
\]

Thus, the **compound interest** is **$630**.

### Summary:
- **Compound Amount** = **$3,630**
- **Compound Interest** = **$630**

Would you like more details or have any questions?

Here are some related questions:
1. What if the interest were compounded quarterly?
2. How does the compound interest formula change with continuous compounding?
3. What if the interest rate was 5% instead of 10%?
4. How does the time period affect the total compound interest?
5. What if the principal amount was $5,000 instead of $3,000?

**Tip:** Compounding more frequently increases the total compound interest gained over time.

Manually calculate the compound amount and compound interest (in $) for the investment. Principal: $3,000, Time Period (years): 2, Nominal Rate (%): 10, Interest Compounded: annually

Learn how to manually calculate the compound amount and compound interest for an investment of $3,000 over 2 years at a 10% annual interest rate. This step-by-step guide uses the compound interest formula to calculate the total amount and interest. Suitable for students in Grades 9-12.

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