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The problem you're working on involves compound interest. The formula used here is:

\[
A = P(1 + r)^t
\]

Where:
- $ A $ is the amount of money in the account after interest,
- $ P $ is the principal (initial amount, $6,000 in this case),
- $ r $ is the annual interest rate (5%, or 0.05 as a decimal),
- $ t $ is the time in years (2.5 years here).

Let's break it down and solve:

1. $ P = 6000 $
2. $ r = 0.05 $
3. $ t = 2.5 $

Substitute the values into the formula:

\[
A = 6000 \times (1 + 0.05)^{2.5}
\]
\[
A = 6000 \times (1.05)^{2.5}
\]
\[
A \approx 6000 \times 1.1276
\]
\[
A \approx 6765.60
\]

So, the approximate value of the account after 2.5 years is **$6,766**. The closest option in the choices given is **$6,778**.

Would you like further clarification or details on any part of this solution?

Here are 5 related questions to expand your understanding:
1. What would the account value be if the interest were compounded monthly instead of annually?
2. How would the formula change if the interest rate were different, say 7%?
3. What happens to the future value if the investment time doubles to 5 years?
4. How does compound interest differ from simple interest, and what would the value be with simple interest?
5. What is the effect of compounding more frequently, like quarterly or monthly?

**Tip:** Compounding frequency significantly affects the total value of an investment. More frequent compounding generally leads to more growth over time.

Mario invested $6,000 in an account that pays 5% annual interest compounded annually. What is the approximate value of the account after 2.5 years?

Learn how to calculate compound interest with a 5% interest rate on a $6,000 investment over 2.5 years. This problem involves key finance concepts and the compound interest formula. Suitable for high school students (Grades 9-12).

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