A company offers a $1000 cash loan to anyone earning a monthly salary of at least $2000. To secure the loan, the borrower signs a contract with a promise to repay the $1000 plus a fixed fee before 3 months have elapsed. Failure to do this gives the company a legal right to take $1540 from the borrower’s next salary before returning any amount that has been repaid.

From past experience, the company predicts that 70% of borrowers succeed in repaying the loan plus the fixed fee before 3 months have elapsed.

a. Calculate the fixed fee that ensures the company an expected 40% profit from each $1000 loan.

b. Assuming that the company charges the fee found in part a, how would it be possible, without changing the loan conditions, for the company’s expected profit from each $1000 loan to be greater than 40%?