You would like to purchase a home and are interested to find out how much you can borrow. When your lender calculates your debt to income ratio, he determines that your maximum monthly payment can be no more than $$3,200.$ You would like to have a $30$ year fully amortizing loan and the interest rate offered on such a loan is currently $8\mathrm{.}5\%.$ Given these constraints, what is the largest loan you can obtain?