A bank makes one-year loans of $25 000 and wants to earn j1 = y% on its whole portfolio of such loans. Each loan is repayable with a single payment (consisting of the amount borrowed plus interest) at the end of one year. Past experience suggests that 85% of the time the borrower will repay the amount borrowed with interest in full, 6% of the time the borrower will repay the full amount borrowed with no interest, 5% of the time the borrower will repay half the amount borrowed with no interest, and 4% of the time the borrower will repay nothing at all. To allow for the default risk, the bank charges an actual rate on these loans of j1 = x% (x>y). Q1 Draw a contingent cash flow diagram to represent the situation above. Q2 Write an expression for the expected value of the loan repayment received on the repayment date. Q3 Write an expression for the loan repayment the bank would like to receive on the repayment date. Q4 If the bank wants to earn j1 = 15% overall, what rate (in j1 form, rounded to two decimal places as a percentage) must it charge for these loans? [25.29% pa]