Jerry is buying a house for $$375,000$ and he has $20\%$ for a down payment. Find the monthly payment necessary to amortize this mortgage if it is financed at $6\mathrm{.}25\%$ for $30$ years. Prepare an amortization schedule for the first two months of his mortgage. How much would be paid for this house if the loan were kept to term? How much would be paid in interest?