Consider a homebuyer$/$investor who plans to buy a new house, the price of which is $$500,000.$ Suppose the buyer does not have any initial savings for the down payment. To buy the house, he needs to borrow $$500,000$ from the bank in the form of a mortgage loan. The mortgage is a $30-$year fixed rate mortgage. After buying the house, the buyer budget is $$30,012$ per year. That is$,$ if the mortgage asks him to repay more than $$30,012$ per year, then he cannot afford it and would choose not to buy this house. Derive the investment of this buyer as a function of interest rate r$.$