Use Table 11-1 to calculate the compound amount (in $) on an investment of $3,500 at 8% interest, compounded semiannually, for 16 years. (Round your answer to the nearest cent.)
$

To calculate the compound amount (A) for an investment using compound interest, we use the formula:

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

Where:
- $ A $ is the compound amount.
- $ P $ is the principal (initial investment) = $3,500.
- $ r $ is the annual interest rate = 8% = 0.08.
- $ n $ is the number of times the interest is compounded per year = 2 (semiannually).
- $ t $ is the time in years = 16.

Let's calculate this step by step. 

### Step 1: Breakdown the formula components:
\[
r/n = 0.08 / 2 = 0.04 \quad \text{(semiannual interest rate)}
\]
\[
nt = 2 \times 16 = 32 \quad \text{(total compounding periods)}
\]

### Step 2: Apply the values to the formula:

\[
A = 3500 \times \left(1 + 0.04\right)^{32}
\]

\[
A = 3500 \times \left(1.04\right)^{32}
\]

Let me calculate the final amount.The compound amount on an investment of $3,500 at 8% interest, compounded semiannually for 16 years, is approximately **$12,278.21**.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this topic:
1. How would the compound amount change if the interest rate was increased to 10%?
2. What would be the result if the interest were compounded quarterly instead of semiannually?
3. How would you calculate the compound interest if the investment duration was shortened to 10 years?
4. What is the difference between simple interest and compound interest in this scenario?
5. How does continuous compounding differ from semiannual compounding?

**Tip:** Compounding frequency has a significant impact on the final amount, with more frequent compounding leading to higher returns over time.

Use Table 11-1 to calculate the compound amount (in $) on an investment of $3,500 at 8% interest, compounded semiannually, for 16 years. (Round your answer to the nearest cent.)

Learn how to calculate the compound amount for an investment of $3,500 at an 8% annual interest rate, compounded semiannually for 16 years. This step-by-step guide explains the compound interest formula and how it applies to semiannual compounding over 16 years, resulting in a final amount of approximately $12,278.21.

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