https://file.aiquickdraw.com/mathbot/file/17282616122394wr1jecb.jpg

To solve the problem, we'll use the compound interest formula, which is given by:

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

Where:
- $A$ is the amount of money accumulated after $n$ periods, including interest.
- $P = 5500$ (the principal investment).
- $r = 8\%$ or $0.08$ (the annual interest rate).
- $n = 2$ (since it's compounded semiannually).
- $t = 16$ (the time in years).

### Step-by-Step Solution:

1. The interest rate per period is $ \frac{r}{n} = \frac{0.08}{2} = 0.04 $.
2. The total number of periods is $nt = 2 \times 16 = 32$.
3. Now, substitute these values into the compound interest formula:

\[
A = 5500 \left(1 + 0.04\right)^{32} = 5500 \times (1.04)^{32}
\]

4. Using a calculator:

\[
(1.04)^{32} \approx 3.999
\]

5. Multiply by the principal amount:

\[
A = 5500 \times 3.999 \approx 21,995.25
\]

### Final Answer:
The compound amount after 16 years is approximately **$21,995.25**.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How would the final amount change if the interest was compounded quarterly instead of semiannually?
2. What is the formula for simple interest, and how would it compare to compound interest over the same period?
3. What happens to the future value if the interest rate increases to 10% while keeping everything else constant?
4. How does the time period $t$ affect the compound interest formula?
5. Can you find the interest earned on this investment by subtracting the principal from the compound amount?

**Tip**: The number of compounding periods significantly impacts the final amount—more frequent compounding leads to more interest accumulation.

Calculate the compound amount on an investment of $5,500 at 8% interest, compounded semiannually, for 16 years.

Learn how to calculate compound interest on an investment of $5,500 at 8% interest, compounded semiannually for 16 years. This step-by-step guide covers key mathematical concepts such as compound interest formulas and exponentiation, suitable for high school students.

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