What is the present value of an ordinary annuity with payments of $\$ 12,000.00$ paid semiannually for 10 years at $6 \%$ compounded semiannually? Assume the interest rate does not change while the account is open. Round your answer to the nearest cent.

Step 1 ：Given an ordinary annuity with payments of $12,000 at the end of every six months for 10 years. The interest rate is 6% compounded semiannually.

Step 2 ：The present value of an annuity can be calculated using the formula: \(PV = P * [(1 - (1 + r)^{-n}) / r]\) where: \(PV\) is the present value, \(P\) is the payment per period, \(r\) is the interest rate per period, and \(n\) is the number of periods.

Step 3 ：In this case, the payment per period (\(P\)) is $12,000, the interest rate per period (\(r\)) is 6% per year compounded semiannually (so 6%/2 = 3% or 0.03 per half-year), and the number of periods (\(n\)) is 10 years * 2 half-years/year = 20 half-years.

Step 4 ：Substitute these values into the formula: \(P = 12000\), \(r = 0.03\), \(n = 20\).

Step 5 ：Calculate the present value: \(PV = 12000 * [(1 - (1 + 0.03)^{-20}) / 0.03]\)

Step 6 ：\(PV = 173,888.671875\)

Step 7 ：Round the final answer to the nearest cent: \(\boxed{173,888.67}\)