To calculate the future value of an investment with compound interest, we use the formula:

$FV = PV \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $FV$ is the future value.
• $PV$ is the present value (initial amount).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times interest is compounded per year.
• $t$ is the time the money is invested for, in years.

For this problem:

• $PV = \$7,000$
• $r = 7\% = 0.07$
• $n = 4$ (since interest is compounded quarterly)
• $t = 7$ years

Now, let's plug these values into the formula:

$FV = 7000 \left(1 + \frac{0.07}{4}\right)^{4 \times 7}$

First, calculate the quarterly interest rate:

$\frac{0.07}{4} = 0.0175$

Next, calculate the total number of compounding periods:

$4 \times 7 = 28$

Now calculate the expression inside the parentheses:

$1 + 0.0175 = 1.0175$

Raise this to the power of 28:

$1.0175^{28} \approx 1.6305068$

Finally, multiply by the initial amount:

$FV = 7000 \times 1.6305068 \approx 11413.55$

So, the future value of $7,000 earning 7% interest compounded quarterly for 7 years is approximately $11,413.55.

Do you want any more details or have any questions?

Here are some related questions:

1. What is the formula for compound interest when compounded monthly?
2. How does the number of compounding periods per year affect the future value?
3. What would be the future value if the interest were compounded annually?
4. How can you calculate the interest earned over a period of time?
5. What is the effective annual rate (EAR) and how is it calculated?
6. How does the future value change with a different interest rate, for example, 5%?
7. What would be the future value if the initial investment was $10,000 instead of $7,000?
8. How can you determine the present value if you know the future value and the interest rate?

Tip: When calculating compound interest, ensure that the interest rate and the number of compounding periods are consistent (e.g., if interest is compounded quarterly, use the quarterly interest rate and the total number of quarters).