3. Determine the amount of each investment. a) 3200 invested at 3% per year,compounded quarterly for 8 years

## Step 1: Convert the annual interest rate to a quarterly rate.<br />### The annual interest rate is 3%, so the quarterly interest rate is $\frac{3\%}{4} = 0.75\% = 0.0075$.<br /><br />## Step 2: Calculate the number of compounding periods.<br />### The investment is compounded quarterly for 8 years, so the number of compounding periods is $4 \times 8 = 32$.<br /><br />## Step 3: Calculate the future value of the investment.<br />### The formula for compound interest is $A = P(1 + r)^n$, where A is the future value, P is the principal, r is the interest rate per compounding period, and n is the number of compounding periods. In this case, $P = \$3200$, $r = 0.0075$, and $n = 32$. Therefore, $A = 3200(1 + 0.0075)^{32} = 3200(1.0075)^{32} \approx 3200(1.2701) \approx 4064.32$.