You have an investment of $5,000 at a quarterly interest rate of 2%. How much will the investment be worth after 1 year?

To calculate the future value of the investment after one year with quarterly compounding, we can use the compound interest formula:

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

Where:
- $ A $ is the future value of the investment
- $ P $ is the principal amount (\$5,000)
- $ r $ is the annual interest rate (which we derive from the quarterly rate)
- $ n $ is the number of compounding periods per year (since it's quarterly, $ n = 4 $)
- $ t $ is the number of years (in this case, $ t = 1 $)

Since the interest rate is given per quarter (2%), the equivalent annual rate is $ r = 4 \times 2\% = 8\% $, or 0.08 as a decimal.

Let's plug in the values:
\[
A = 5000 \left( 1 + \frac{0.08}{4} \right)^{4 \times 1}
\]

Now I'll calculate this step-by-step.

Find out how to calculate the future value of a $5,000 investment with a 2% quarterly interest rate over 1 year using the compound interest formula. This problem demonstrates key financial and algebraic concepts, suitable for students in Grades 9-12.

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