Southwest Dry Cleaners believes that it will need new equipment in $7$ years. The equipment will cost $$26,000.$ What lump sum should be invested today at $4\%$ compounded semiannually, to yield $$26,000?$ Round to the nearest cent.

A$.$ $$22,724\mathrm{.}26$

B$.$ $$19,704\mathrm{.}75$

C$.$ $$24,125\mathrm{.}84$

D$.$ $$22,611\mathrm{.}20$