If $2000 is invested for x years at 8%, compounded quarterly, the future value that will result is represented by the following equation.
S = 2000(1.02)4x
What amount will result in 6 years

To find the future value $ S $ of the investment after 6 years, we'll use the given formula:

\[
S = 2000(1.02)^{4x}
\]

where:
- $ 2000 $ is the initial investment (principal),
- $ 1.02 $ is the growth factor per quarter (since it's compounded quarterly),
- $ 4x $ represents the total number of quarters, with $ x $ being the number of years.

For $ x = 6 $, the number of quarters is:

\[
4x = 4 \times 6 = 24
\]

Now, substitute $ x = 6 $ into the equation:

\[
S = 2000(1.02)^{24}
\]

First, calculate $ 1.02^{24} $:

\[
1.02^{24} \approx 1.60844
\]

Now, multiply by the principal $ 2000 $:

\[
S = 2000 \times 1.60844 \approx 3216.88
\]

Therefore, the future value of the investment after 6 years is approximately **$3216.88**.

Would you like further details or have any questions?

### Related Questions:
1. How does changing the interest rate affect the future value?
2. What if the interest were compounded monthly instead of quarterly?
3. What would be the future value if the investment period were 10 years?
4. How does the formula change if the compounding frequency is different?
5. What would the future value be if the principal were $5000?

**Tip:** When dealing with compound interest, the frequency of compounding has a significant impact on the future value, with more frequent compounding leading to greater growth.

If $2000 is invested for x years at 8%, compounded quarterly, the future value that will result is represented by the following equation. S = 2000(1.02)^{4x}. What amount will result in 6 years?

This detailed explanation shows how to calculate the future value of a $2000 investment over 6 years at an 8% annual interest rate, compounded quarterly. Learn how the formula S = 2000(1.02)^{24} results in a future value of $3216.88. Suitable for students in Grades 10-12.

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