What wold be the amount of coumpound interest on $8,000 invested for one year at 6%,compounded quaterly? Round your answer to the nearest dollar.

6/4 = 1.5 percent every three months

1.015^4 = 1.0614
or 6.14 percent in a year
8,000 * .0614 = $491

To calculate the compound interest on an investment, we can use the compound interest formula:

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

Where:
A represents the total amount including the principal and interest,
P is the principal amount (the initial investment),
r is the annual interest rate (expressed as a decimal),
n is the number of times interest is compounded per year, and
t is the number of years.

In this case, the principal amount (P) is $8,000, the annual interest rate (r) is 6% (or 0.06 as a decimal), the interest is compounded quarterly (n = 4), and the investment is for 1 year (t = 1).

Plugging these values into the compound interest formula, we get:

A = 8000(1 + 0.06/4)^(4*1)

Now, let's calculate the compound interest:

A = 8000(1 + 0.015)^4
= 8000(1.015)^4
= 8000(1.061676)
≈ $8,493

To find the compound interest, we subtract the principal amount from the total amount including interest:

Compound Interest = A - P
= $8,493 - $8,000
≈ $493

Therefore, the compound interest on an $8,000 investment for one year at an annual interest rate of 6%, compounded quarterly, is approximately $493.