A bank is evaluating a $$15,000$ loan application for a $2-$

year term. The risk model suggests:

a$)50\%$ chance of full repayment with interest

b$)35\%$ chance of repaying $60\%$ of the total owed

c$)15\%$ chance of no repayment

What is the probability of the borrower not repaying

anything?

For a $$20,000$ unsecured loan over $18$ months, a bank's

risk model predicts:

a$)55\%$ chance of full repayment with interest

b$)25\%$ chance of repaying $75\%$ of the total owed

c$)20\%$ chance of no repayment

What interest rate should the bank charge to achieve a

risk$-$adjusted return of $2\%?$

A bank is considering a $$12,000$ loan for $1$ year. The risk

model indicates:

a$)40\%$ chance of full repayment with interest

b$)40\%$ chance of repaying $40\%$ of the total owed plus

collateral

c$)20\%$ chance of no repayment, but the bank gets the

collateral

If the maximum allowed interest rate is $25\%,$ what

minimum collateral value is needed?