Suppose that a family's annual income is $$50,000.$ Financial experts recommend that mortgage payments not exceed $25\%$ of a family's income. $(3$ points$).$

a$)$ According to the experts, what is the maximum monthly mortgage payment that the family can afford?

b$)$ Assuming an annual mortgage interest rate of $7\%$ rate compounded monthly for a $30$year mortgage with the monthly payments that you already calculated, how large a mortgage can the family afford?