You have found your dream home. The selling price is $$500,000.$ You will put $$100,000$ as down payment and obtain a $30-$year fixed$-$rate mortgage loan at $6$ percent annual interest rate from a bank for the rest.

a$)$ You are required to make an equal payment every month for $360$ months to pay off the balance on the loan. Assume that the first payment begins in one month after you have obtained the loan. What will each monthly payment be$?$

b$)$ If you want to pay off the remaining principal on your mortgage loan after $10$ years $($i$.$e$.,120$ months$),$ how much will you have to pay? Assume that you have never missed your payments during the first ten years after you have obtained the loan. The bank imposes no charges for early payoff of the loan.