Find the highest interest rate:
There are 2 entrepreneurs, Sally and Paul. The return to their projects are given by:
To finance the project, each entrepreneur needs to borrow from a bank an initial capital of 100. The loan contract stipulates that if the project return is high, then the firms pays principal plus interests, and if the project return is low, then the bank seizes whatever value that the firm has left over. Find the highest interest rate at which Sally is willing to borrow, the highest interest rate at which Paul is willing to borrow, and the bank's expected net profit if the interest rate is 10% and 18%, respectively.