When Jane and Patrick Baker were house hunting $5$ years ago, the fixed rate on a $30-$ year mortgage was $6\%$ with monthly compounding. After checking many houses, they finally decided to buy a home for $$500,000.$ The couple decided to pay a $20\%$ down payment and took a $30-$year mortgage with monthly payments. What is Jane and Patrick$$s monthly mortgage payment?

$$2600$

$$2500$

$$2300$

$$2400$