The chance of default is independent across all the loans


Consider two banks. Bank A has 1000 loans outstanding each for $100,000, which it expects to be fully repaid today. Each of Bank A's loans has a 6% probability of default, in which case the bank will receive $0 for each of the defaulting loans. Bank B has 100 loans of $1 million outstanding, which it also expects to be fully repaid today. Each of Bank B's loans has a 5% probability of default, in which case the bank will receive $0 for each of the defaulting loans. The chance of default is independent across all the loans. What is the expected overall payoff to Bank A?

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Financial Management: The chance of default is independent across all the loans
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