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To solve this, we need to use the formula for compound interest:

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

where:
- $ A $ is the amount of money after $ t $ years,
- $ P $ is the principal (initial amount),
- $ r $ is the annual interest rate (in decimal form),
- $ n $ is the number of times interest is compounded per year,
- $ t $ is the number of years.

### Given Values
- Principal $ P = 6000 $
- Rate $ r = 5\% = 0.05 $
- Time $ t = 4 $ years

#### (a) Compounded Annually
Since compounding is annual, $ n = 1 $.

Using the formula:
\[
A = 6000 \left(1 + \frac{0.05}{1}\right)^{1 \times 4}
\]
\[
A = 6000 \left(1 + 0.05\right)^4
\]
\[
A = 6000 \times (1.05)^4
\]

Calculating $ (1.05)^4 $ and then multiplying by 6000:

\[
A \approx 6000 \times 1.21550625
\]
\[
A \approx 7293.04
\]

### Answer
The amount after 4 years with annual compounding is approximately **$7293.04**.

Would you like further details or have any additional questions?

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Here are some related questions:
1. What is the amount if compounded semiannually?
2. How does the future value change with different compounding frequencies?
3. What would the amount be if compounded quarterly?
4. How does an increase in interest rate impact the future value?
5. What if the interest rate was 7% instead of 5%?

**Tip:** Always double-check your calculations, especially when compounding frequencies differ.

For each deposit, find the future value (that is, the final amount on deposit) when compounding occurs (a) annually, (b) semiannually, and (c) quarterly. Given: Principal = $6000, Rate = 5%, Time = 4 years. (a) If it is compounded annually, what is the amount after 4 years?

Learn how to calculate the future value of a $6000 deposit at a 5% interest rate compounded annually over 4 years. This problem involves compound interest formulas and exponential growth, making it suitable for high school students.

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