A man deposits $\$ 18,000$ at the beginning of each year for 10 years in an account paying $8 \%$ compounded annually. He then puts the total amount on deposit in another account paying $9 \%$ compounded semiannually for another 9 years. Find the final amount on deposit after the entire 19-year period.

He will have a final amount of $\$ \square$ after the entire 19-year period. (Simplify your answer. Round to the nearest cent as needed.)

Step 1 ：For the first 10 years, the man deposits $18,000$ at the beginning of each year in an account paying $8\%$ compounded annually. The future value of these deposits can be calculated using the formula for the future value of a series of annuity payments made at the beginning of each period: \(FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)\), where \(P\) is the payment amount, \(r\) is the interest rate per period, and \(n\) is the number of periods. Substituting the given values, we get \(FV = 18000 \times \left(\frac{(1 + 0.08)^{10} - 1}{0.08}\right)\).

Step 2 ：Calculating the above expression, we get \(FV \approx \$245,886.58\). This is the total amount the man has in his account after 10 years.

Step 3 ：For the next 9 years, the man puts the total amount on deposit in another account paying $9\%$ compounded semiannually. The future value of this deposit can be calculated using the formula for the future value of a single lump sum compounded more than once per year: \(FV = P \times (1 + r/n)^{nt}\), where \(P\) is the principal amount, \(r\) is the annual interest rate, \(n\) is the number of times interest is compounded per year, and \(t\) is the time in years. Substituting the given values, we get \(FV = 245886.58 \times (1 + 0.09/2)^{2 \times 9}\).

Step 4 ：Calculating the above expression, we get \(FV \approx \$593,848.86\). This is the total amount the man has in his account after the entire 19-year period.

Step 5 ：So, the man will have a final amount of \(\boxed{\$593,848.86}\) after the entire 19-year period.