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The question displayed in the image involves calculating the amount of money in a savings account after compound interest over time. Here is how we can approach solving it step-by-step:

### Given Information:
- **Principal (P)** = $8000
- **Rate (r)** = 3% annually = 0.03
- **Compounded annually**
- **Time (t)** = 3 years

### Formula for Compound Interest:
The compound interest formula is:

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

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

Since the interest is compounded annually, $n = 1$. Thus, the formula simplifies to:

\[
A = P \left(1 + r\right)^t
\]

### Part A: Calculating the total amount after 3 years:
Substituting the given values into the formula:

\[
A = 8000 \left(1 + 0.03\right)^3
\]
\[
A = 8000 \times (1.03)^3
\]
\[
A = 8000 \times 1.092727
\]
\[
A \approx 8741.82
\]

So, the amount of money in the account after 3 years is **$8741.82**.

### Part B: Calculating the interest earned:
The interest earned is the total amount minus the principal:

\[
\text{Interest} = A - P
\]
\[
\text{Interest} = 8741.82 - 8000
\]
\[
\text{Interest} = 741.82
\]

Thus, the interest earned after 3 years is **$741.82**.

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Do you need any further clarification or additional details? Here are 5 related questions you could explore next:

1. How does the frequency of compounding affect the final amount in an account?
2. What would be the amount after 5 years instead of 3 years?
3. How would the interest calculation change if the rate was compounded quarterly?
4. How is continuous compounding different from annual compounding?
5. What happens if the interest rate is 5% instead of 3%?

**Tip**: Always double-check whether interest is compounded annually, semi-annually, or more frequently, as it significantly affects the results.

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. A. Find how much money there will be in the account after the given number of years. B. Find the interest earned. Principal: $8000, Rate: 3% compounded annually, Time: 3 years.

Learn how to calculate the compound interest on $8000 at a 3% annual rate for 3 years. The solution includes step-by-step details on finding the total amount and the interest earned using the compound interest formula. Suitable for high school students (Grades 9-12).

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