400 Parker invested 5000 for 12 years at 9% interest compounded quarterly. How much money will he have made at the end of 12 years? Show all your work.

## Step 1: Convert the interest rate to a decimal and find the quarterly interest rate.<br />### The annual interest rate is 9%, which is $9/100 = 0.09$ in decimal form. Since the interest is compounded quarterly, we divide the annual rate by 4 to find the quarterly interest rate: $0.09/4 = 0.0225$.<br /><br />## Step 2: Calculate the number of compounding periods.<br />### The investment is for 12 years and the interest is compounded quarterly (4 times per year). Therefore, the number of compounding periods is $12 \times 4 = 48$.<br /><br />## Step 3: Calculate the final amount using the compound interest formula.<br />### The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, $P = \$5000$, $r = 0.09$, $n = 4$, and $t = 12$. Plugging these values into the formula, we get:<br />$A = 5000(1 + \frac{0.09}{4})^{4 \times 12} = 5000(1 + 0.0225)^{48} = 5000(1.0225)^{48} \approx 5000(2.917757) \approx 14588.79$.