A couple has just purchased a home for $$402,100\mathrm{.}00.$ They will pay $20\%$ down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of $6\mathrm{.}00\%$ APR with monthly compounding. The mortgage has a term of $30$ year$.$

What is the monthly payment on the loan?

Answer format: Currency: Round to: $2$ decimal places.