$1.$ You purchased a new house for $$450,000$ and financed the purchase with a $$400,000$ mortgage, payable monthly over $15$ years at a yearly rate of $7\mathrm{.}0\%.$A$.$How much are your monthly payments, assuming you made your first payment at the end of the first month? B$.$How much do you owe on this house after making $10$ years of monthly payments?