Find the future value of the following annuity due.
Payments of $\$ 1000$ for 2 years at $4 \%$ compounded semiannually
\[
\mathrm{S} \approx \$
\]
(Round to the nearest cent as needed.)

Step 1 ：We are given that the payments are $1000, the annual interest rate is 4% or 0.04 in decimal form, the interest is compounded semiannually so n = 2, and the time the money is invested for is 2 years.

Step 2 ：We can find the future value of the annuity due using the formula: \[S = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) \times (1 + r/n)\]

Step 3 ：Substituting the given values into the formula, we get: \[S = 1000 \times \left( \frac{(1 + 0.04/2)^{2*2} - 1}{0.04/2} \right) \times (1 + 0.04/2)\]

Step 4 ：Solving the above expression, we find that the future value of the annuity due is approximately $4204.04.

Step 5 ：\(\boxed{4204.04}\) is the future value of the annuity due.