Myrna deposits $$1,000$ in a savings account. The money is left on deposit for $2$ years earning $4\%$ compounded semiannually. Calculate the account balance at the end of $2$ years. Do not round intermediate results.

$$1,081\mathrm{.}60$

$$1,080\mathrm{.}00$

$$1,097\mathrm{.}63$

$$1,082\mathrm{.}43$