Question

wo-part question. Only answer number 2, please.

1. There are two types of borrowers in the credit market for motorcycle loans, type X, and type R. They both need a loan for $37,600, for a Ducati. Type X repays 96% of the time and type R repays 84% of the time. If the lending bank, Street Bank, has full information, then the risk premium for X is ____% and for R it is ____%.

2. Consider the credit market in the previous question again, with type X and R, but now assume Street Bank cannot observe type prior to issuing the loan. Street Bank figures the population of borrowers is divided up such that 35% are type X and the rest are type R. In this case, the competitive pooling rate on the motorcycle loans is? A. 11.95% B. 12.65% C. 12.9% D. 13.4%

Answer 1

Bank pays $37600 loan to a borrower who is either type X or type R. Pooling rate of interest is z% so type X as well as type R will be paying 37600 + z%*37600 = 37600(1 + z%) if they pay, at all. When borrower is Type X, she pays with 96% probability and when she is type R, she pays with a probability of 84%. Hence expected amount paid when she is type X is 96%*37600(1 + z%) and expected amount paid when she is type R is 84%*37600(1 + z%). Type X are 35% and type R are 65%.

Hence we have

37600 = 96%*37600(1+z%)*35% + 84%*37600(1+z%)*65%

37600 = 12633.6 + 126.336z + 20529.6 + 205.296z

4436.8 = 331.632z

z = 13.4%

Select D.