Brian invests $4,000 at 12% interest compounded quarterly for 12 years.

which bank is that? I'll put my money there!

Me, too ... yowza!!

12/4 = 3

4,000 * 1.03^48

To find the future value of Brian's investment, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = future value of the investment
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

In this case:
P = $4,000
r = 12% or 0.12 (remember to convert from percentage to decimal)
n = 4 (compounded quarterly)
t = 12 years

Let's plug these values into the formula:

A = 4000(1 + 0.12/4)^(4*12)

First, divide the annual interest rate by the number of times it is compounded per year:
0.12/4 = 0.03

Next, multiply the exponent by the number of times the interest is compounded per year:
4*12 = 48

Now, simplify and calculate the final value:

A = 4000(1 + 0.03)^48

Using a calculator, evaluate the expression on the right side of the equation:
(1 + 0.03)^48 ≈ 2.208040

Multiply the principal amount by the evaluated expression:

A ≈ 4000 * 2.208040 ≈ $8,832.16

Therefore, the future value of Brian's investment after 12 years would be approximately $8,832.16.