Find the compound amount for the deposit and the amount of interest earned.
​$4000 at 6​% compounded annually for 3 years
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Part 1
The compound amount after 3 years is ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To calculate the compound amount for a deposit, you can use the formula for compound interest:

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

Where:
- $ A $ = the future value (compound amount),
- $ P $ = the initial principal (deposit),
- $ r $ = annual interest rate (as a decimal),
- $ n $ = number of times the interest is compounded per year,
- $ t $ = the number of years.

### Given:
- $ P = 4000 $ (the initial deposit),
- $ r = 6\% = 0.06 $ (annual interest rate),
- $ n = 1 $ (compounded annually),
- $ t = 3 $ years.

Now, substitute the values into the formula:

\[
A = 4000 \left( 1 + \frac{0.06}{1} \right)^{1 \times 3}
\]
\[
A = 4000 \left( 1 + 0.06 \right)^3
\]
\[
A = 4000 \left( 1.06 \right)^3
\]
\[
A = 4000 \times 1.191016
\]
\[
A \approx 4764.06
\]

Thus, the compound amount after 3 years is approximately **$4764.06**.

### Part 2: Calculating the interest earned
The interest earned is the difference between the compound amount and the initial deposit:

\[
\text{Interest} = A - P = 4764.06 - 4000 = 764.06
\]

Thus, the interest earned is **$764.06**.

### Summary:
- Compound amount: **$4764.06**
- Interest earned: **$764.06**

Would you like further details on how this formula works?

Here are some related questions you might find useful:
1. What would the compound amount be for 5 years instead of 3?
2. How would the result change if the interest was compounded monthly instead of annually?
3. What is the formula for continuous compound interest?
4. How does compound interest differ from simple interest?
5. What would happen if the interest rate was 4% instead of 6%?

**Tip:** Always verify the frequency of compounding to ensure correct calculations!

Find the compound amount for the deposit and the amount of interest earned. $4000 at 6% compounded annually for 3 years.

Learn how to calculate the compound amount for a $4000 deposit at a 6% annual interest rate compounded annually over 3 years. This step-by-step guide includes key concepts like the compound interest formula and how to calculate the total interest earned. Suitable for students in Grades 9-12.

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