Huy opened a new savings account. He deposited $$40,000$ at $10\%$ compounded semiannually. At the start of the fourth year, Huy depos an additional $$20,000$ that is also compounded semiannually at $10\%.$ At the end of six years, the balance in Huy's account is $($use the tab in the handbook$)$:

$$53,604\mathrm{.}00$

$$80,406\mathrm{.}00$

None of these

$$73,604\mathrm{.}00$

$$98,636\mathrm{.}72$