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To solve this compound interest problem, let's break down the information and apply the compound interest formula.

### Given Data:
- **Principal (P)**: $340
- **Annual Interest Rate (r)**: 2.4% or 0.024 as a decimal
- **Compounded Semiannually**: This means the interest is compounded twice a year, so $ n = 2 $.
- **Time (t)**: 15 years

### Compound Interest Formula
The compound amount $ A $ after $ t $ years is calculated by:
\[
A = P \left(1 + \frac{r}{n}\right)^{n \cdot t}
\]
where:
- $ P $ is the principal,
- $ r $ is the annual interest rate,
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the time in years.

### Substituting Values
Let's plug in the values:
\[
A = 340 \left(1 + \frac{0.024}{2}\right)^{2 \times 15}
\]

1. **Calculate $ \frac{0.024}{2} $**:
   \[
   \frac{0.024}{2} = 0.012
   \]

2. **Update the formula with this result**:
   \[
   A = 340 \left(1 + 0.012\right)^{30}
   \]

3. **Simplify inside the parentheses**:
   \[
   A = 340 \left(1.012\right)^{30}
   \]

4. **Calculate $ (1.012)^{30} $**:
   \[
   (1.012)^{30} \approx 1.42576
   \]

5. **Multiply by the principal**:
   \[
   A \approx 340 \times 1.42576 \approx 485.76
   \]

### Result
The compound amount after 15 years is approximately **$485.76**.

### Interest Earned
The interest earned is the compound amount minus the initial principal:
\[
\text{Interest} = A - P = 485.76 - 340 = 145.76
\]

### Final Answer
- **Compound Amount**: $485.76
- **Interest Earned**: $145.76

Would you like further explanation on any steps?

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### Additional Practice Questions
1. If the rate were 3% compounded quarterly, what would the compound amount be after 10 years?
2. How much would the compound amount be if $500 were invested at 4% interest compounded monthly for 5 years?
3. What would the total compound interest be if $1,000 were invested at 5% interest compounded annually for 20 years?
4. How does changing the compounding frequency to daily affect the total compound amount?
5. Calculate the compound amount for a $600 deposit at 3.5% interest compounded semiannually for 8 years.

### Tip
When dealing with compound interest problems, carefully identify the compounding frequency (semiannually, quarterly, monthly, etc.) since it significantly affects the total amount.

Find the compound amount for a deposit of $340 at 2.4% interest compounded semiannually for 15 years, and calculate the amount of interest earned.

Calculate the compound amount and interest earned on a $340 deposit at 2.4% interest compounded semiannually over 15 years. This problem demonstrates the compound interest formula and exponential growth, suitable for high school students in Grades 9-12.

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