You put $20\%$ down on a home with a purchase price of $$500,000.$ The down payment is thus $$100,000,$ leaving a balance owed of $$400,000.$ A bank will loan you this remaining balance $($$$400,000)$ at $6\mathrm{.}90\%$ APR. You will make monthly end$-$of$-$the$-$period payments with a $30-$year payment schedule. What is the monthly payment under this schedule?

$$2,634\mathrm{.}4$

$$2,465\mathrm{.}5$

$$2,575\mathrm{.}3$

$$2,345\mathrm{.}25$

$$2,270\mathrm{.}5$