With interest rates at $4\mathrm{.}875\%$ for a $30-$year fixed mortgage, Dan, age $48,$ plans to buy a house for $$825,000.$ He wants to put half of the purchase price down. What will his monthly mortgage payment be for principal and interest?

$$2,182\mathrm{.}98.$

$$2,768\mathrm{.}55.$

$$3,176\mathrm{.}43.$

$$3,493\mathrm{.}67.$