Question: What is the minimum interest rate the bank should charge if the bank wants to break even? - Assume the size of loan is 100. - Notation: r = interest rate it = profit Exp (11') = expected profit 3 = principal + interest = 100(1 + r) Question: which borrowers find this interest rate profitable? - ifr = 33.3%, which borrowers are going to borrow? - Safe projects pays 150 with probability 100% - Safe borrowers, ifr = 33.3%, have to pay back 133.3. - 150 133.3 2::- [l - Therefore, it is still profitable. - Risky project pays 280 with probability 50% and zero with probability of 50%. [0.5 * (280 1333)] + [0.5 at 0] I} 0. It is also profitable. - But, in reality, we have excess demand for credit. . Calculate the bank expected profit as a function of the interest rate: Exp(n) = [P(borrower has safe project) * B] + [P(borrower has risky project) * B * p(risky project gives high return)] - 100 Exp (It) = [0.5 * B] + [0.5 * B * 0.5] - 100 = 0.5B + 0.25B - 100 = 0. 75B - 100 . Find r that gives Exp () = zero 0.75B = 100 = B=133.3 B = 100(1 +r) = 100(1 + r) = 133.3 r = 33.3%