What are the future value and the interest earned if $3000 is invested for 4 years at 8% compounded quarterly? (Round your answers to the nearest cent.)
future value	$
interest earned    	$

To calculate the future value and the interest earned for an investment compounded quarterly, we can use the formula for compound interest:

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

Where:
- $A$ is the future value (what we're solving for),
- $P$ is the principal (initial investment) = $3000,
- $r$ is the annual interest rate (8% or 0.08),
- $n$ is the number of times the interest is compounded per year (quarterly means $n = 4$),
- $t$ is the time in years = 4.

### Step 1: Calculate the future value $A$
\[
A = 3000 \left(1 + \frac{0.08}{4}\right)^{4 \times 4}
\]
\[
A = 3000 \left(1 + 0.02\right)^{16}
\]
\[
A = 3000 \times (1.02)^{16}
\]
\[
A \approx 3000 \times 1.3686
\]
\[
A \approx 4105.80
\]

### Step 2: Calculate the interest earned
The interest earned is simply the future value minus the principal:
\[
\text{Interest earned} = A - P = 4105.80 - 3000 = 1105.80
\]

### Final Answer:
- **Future Value** = \$4105.80
- **Interest Earned** = \$1105.80

Would you like more details on any step, or do you have any questions?

Here are some related questions for you:
1. How does changing the compounding frequency affect future value?
2. What is the future value if the interest rate increases to 10%?
3. How would the calculation differ if compounded monthly instead of quarterly?
4. What is the formula for simple interest, and how does it compare to compound interest?
5. What if the investment period was extended to 6 years instead of 4?

**Tip**: The more frequently the interest is compounded, the higher the future value of the investment will be.

What are the future value and the interest earned if $3000 is invested for 4 years at 8% compounded quarterly? (Round your answers to the nearest cent.)

Learn how to calculate the future value and interest earned for an investment of $3000 at 8% compounded quarterly over 4 years. This problem covers the compound interest formula, demonstrating how exponential growth applies to financial calculations. Step-by-step solutions provided. Suitable for students in Grades 10-12.

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