I am supposed to solve the following problem.
The bank provides 1,000 dollars loans. Risk-free clients will repay the loan in full for a year, in addition to paying 4% interest. For a high-risk client, there is a 30% chance that he will not pay anything and an 70% chance that he will repay the loan in full and 30% interest.
Assume that the government has guaranteed to the bank that in the event of non-payment of the loan, it will repay the bank's principal, that means 1,000$.
What costs will the government have?
So I understand that the cost of the government will be 1,000 dollars, but I do not know with what probability. I should calculate the expected cost.
Can anyone help?
The expected cost is of $1000\$\times 0.3\times(\text{number of high-risk clients})$ per year.