I need help with the steps to answer this question.

(12 points) 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 a 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 $ 30,011 per year. That is, if the mortgage asks him to repay more than $ 30,011 per year (this happens when the interest rate is too high), 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