A homeowner could take out a $15-$year mortgage at a $3$ percent annual rate on a $$260,000$ mortgage amount, or she could finance the purchase with a $30-$year mortgage at a $4$ percent annual rate. How much total interest over the entire mortgage period could she save by financing her home with the $15-$year mortgage $($to the nearest dollar$)?$

$$190,105$

$$138,612$

$$230,408$

$$144,325$

$$123,669$