How much interest is included in the future value of an ordinary simple annuity of $\$ 1,600$ paid every six months at $7 \%$ compounded semi-annually if the term of the annuity is 4 years? The interest is $\$ \square$ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Given that the annuity payment (P) is $1600, the annual interest rate (r) is 7% or 0.07 in decimal form, the number of times that interest is compounded per year (n) is 2, and the time the money is invested for in years (t) is 4 years.

Step 2 ：The future value of the annuity (FV) can be calculated using the formula: \(FV = P \times \left[(1 + \frac{r}{n})^{nt} - 1\right] \div \frac{r}{n}\)

Step 3 ：Substituting the given values into the formula, we get: \(FV = 1600 \times \left[(1 + \frac{0.07}{2})^{2 \times 4} - 1\right] \div \frac{0.07}{2}\)

Step 4 ：Calculate the future value (FV) to get approximately $14482.70

Step 5 ：The total amount of payments made is calculated by multiplying the annuity payment (P) by the number of times that interest is compounded per year (n) and the time the money is invested for in years (t). So, the total payments = P * n * t = $1600 * 2 * 4 = $12800

Step 6 ：The interest included in the future value of the annuity is then calculated by subtracting the total amount of payments made from the future value of the annuity. So, the interest = FV - total payments = $14482.70 - $12800

Step 7 ：Calculate the interest to get approximately $1682.70

Step 8 ：Final Answer: The interest included in the future value of the annuity is \(\boxed{\$1682.70}\) (rounded to the nearest cent).