Using Table 11-1, calculate the compound amount and compound interest (in $) for the investment. (Round your answers to the nearest cent.)
Principal	Time
Period (years)	Nominal
Rate (%)	Interest
Compounded	Compound
Amount	Compound
Interest
$6,000	4	12	annually	$
Incorrect: Your answer is incorrect.
$
Incorrect: Your answer is incorrect.

To calculate the compound amount and compound interest for an investment with a principal of $6,000, a time period of 4 years, a nominal interest rate of 12%, and annual compounding, we'll use the compound interest formula:

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

Where:
- $ A $ is the compound amount (the total value of the investment after interest is applied),
- $ P $ is the principal (initial investment amount),
- $ r $ is the nominal interest rate (as a decimal),
- $ n $ is the number of times interest is compounded per year,
- $ t $ is the time the money is invested for (in years).

### Given values:
- $ P = 6,000 $,
- $ r = 12\% = 0.12 $,
- $ t = 4 $ years,
- $ n = 1 $ (since the interest is compounded annually).

### Step 1: Calculate the Compound Amount

Using the formula:

\[
A = 6000 \left( 1 + \frac{0.12}{1} \right)^{1 \times 4}
\]

\[
A = 6000 \left( 1.12 \right)^{4}
\]

I'll calculate this value.The compound amount after 4 years is approximately **$9,441.12**.

### Step 2: Calculate the Compound Interest
The compound interest is the difference between the compound amount and the principal.

\[
\text{Compound Interest} = A - P = 9,441.12 - 6,000
\]

Let's calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can easily calculate the compound interest manually using this formula:

\[
\text{Compound Interest} = 9,441.12 - 6,000 = 3,441.12
\]

So the compound interest is approximately **$3,441.12**.

Would you like more details or have any questions about this? Here are 5 related questions to expand your understanding:

1. How does the frequency of compounding affect the compound amount?
2. What is the formula for continuously compounded interest?
3. How would the results change if the interest was compounded monthly instead of annually?
4. Can you calculate the future value of the investment if the interest rate were different?
5. How can compound interest be used in loan calculations?

**Tip:** The more frequently interest is compounded, the larger the compound amount will be, as the interest is being calculated and added to the principal more often.

Using Table 11-1, calculate the compound amount and compound interest (in $) for the investment. (Round your answers to the nearest cent.) Principal: $6,000, Time Period: 4 years, Nominal Rate: 12%, Interest Compounded: annually.

Learn how to calculate the compound amount and compound interest for a $6,000 investment over 4 years with a 12% nominal rate compounded annually. This step-by-step guide uses the compound interest formula to determine the final amount and interest earned, ideal for high school students studying finance and exponential growth.

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