Consider again an economy like the one described in exercise 6. But now suppose that at date 1, with the same probability π = 1/3, the borrower can turn out to be type 1, type 2, or type 3. Type 1 can get a gross return of \($300\) with certainty, type 2 can get a gross return of \($350\) with probability p2 = 0.75, and type 3 can get a gross return of \($400\) with probability p3 = 0.5. Assume that the opportunity cost for all borrowers is zero. Compute the interest charged by the bank. Will all agents be able to borrow? Explain your answer.