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The formula provided for compound interest is:

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

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

### Given values:
- $ P = 1000 $ (the principal amount invested),
- $ r = 0.08 $ (8% annual interest rate),
- $ n = 4 $ (since interest is compounded quarterly),
- $ t = 5 $ years.

Now, substitute these values into the formula:

\[
A(5) = 1000 \left(1 + \frac{0.08}{4} \right)^{4 \times 5}
\]

First, simplify the fraction inside the parentheses:

\[
\frac{0.08}{4} = 0.02
\]

Now the equation becomes:

\[
A(5) = 1000 \left(1 + 0.02 \right)^{20} = 1000 \left(1.02 \right)^{20}
\]

Now calculate $ 1.02^{20} $:

\[
1.02^{20} \approx 1.485947
\]

Thus:

\[
A(5) \approx 1000 \times 1.485947 = 1485.95
\]

### Final answer:
The amount accumulated after 5 years is **$1,485.95**.

Would you like more details on the steps, or do you have any other questions?

### Related questions:
1. How would the final amount change if the interest was compounded monthly?
2. What if the investment was made for 10 years instead of 5?
3. How does the formula change if the interest is compounded continuously?
4. What would be the interest earned (excluding the principal) in this scenario?
5. How does the annual percentage yield (APY) compare to the nominal interest rate in this case?

### Tip:
Remember that compound interest grows faster when compounded more frequently (e.g., monthly vs. annually), which is key to understanding long-term investments.

Determine the amount of money accumulated after 5 years if $1,000 is invested in an account that pays 8% interest compounded quarterly. Round to the nearest cent.

Learn how to calculate compound interest with a principal of $1,000 at an 8% interest rate, compounded quarterly for 5 years. This solution involves using the compound interest formula to find the accumulated amount, suitable for high school students in Grades 9-12.

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