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.### The annual interest rate is 3%, so the quarterly interest rate is .## Step 2: Calculate the number of compounding periods.### The investment is compounded quarterly for 8 years, so the number of compounding periods is .## Step 3: Calculate the future value of the investment.### The formula for compound interest is , 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, 3200 r = 0.0075 n = 32 A = 3200(1 + 0.0075)^{32} = 3200(1.0075)^{32} \approx 3200(1.2701) \approx 4064.32$.