chad's commission rate is 12%. He invests his commission from the sale of $9000 worth of merchandise at an interest rate of 8%, compounded quarterly. How much is Chad's investment worth after 6 months?

.12 * 9000 = 1080 invested

interest rate per quarter = 8/4 = 2%
two quarters is six months
so 1.02 * 1.02 = 1.0404
1.0404 * 1080 = $ 1123.63

commission = .12(9000) = 1080

1080(1.02)^2
= ...

( rate = .08/4 = .02 , number of quarters in 6 months = 2 )

To find out how much Chad's investment is worth after 6 months, we need to calculate the compound interest on his investment.

First, let's calculate the commission that Chad earned from the sale of $9000 worth of merchandise. Chad's commission rate is 12%, so we can find his commission amount by multiplying $9000 by 12% (or 0.12):

Commission = $9000 * 0.12 = $1080

Chad then decides to invest his commission at an interest rate of 8%, compounded quarterly. The formula to calculate compound interest is:

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

Where:
A is the final amount after compound interest
P is the principal amount (the initial investment)
r is the interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the time in years

In Chad's case, the principal amount (P) is $1080, the interest rate (r) is 8% (or 0.08), and the time (t) is 6 months (or 0.5 years). The interest is compounded quarterly, so the number of times interest is compounded per year (n) is 4.

Let's plug in these values into the compound interest formula:

A = 1080 * (1 + 0.08/4)^(4 * 0.5)

Calculating the expression inside the parentheses:

(1 + 0.08/4) = 1.02

Plugging this value back into the formula:

A = 1080 * 1.02^(4 * 0.5)

Simplifying further, we have:

A = 1080 * 1.02^2

Calculating 1.02 raised to the power of 2:

A = 1080 * 1.0404

Finally, multiplying the principal amount by the result:

A = $1,121.87

Therefore, after 6 months, Chad's investment will be worth approximately $1,121.87.