Assume risk-neutrality and that the appropriate interest rate is 8%. You believe your probability of defaulting on a loan and repaying nothing is only 5%, but your bank believes it
Is 20%. What rate will the bank quote you on a loan?

Question

Quizplus · Accepted Answer

The bank will quote a rate that covers their expected losses from default. The expected value of the loan is E(V) = (1-0.05)*the loan amount + 0.05*0 = 0.95*the loan amount. The bank will want to earn the appropriate interest rate of 8% plus a premium to cover their losses from default. Therefore, the bank's quoted rate will be (0.08 + premium)/0.95 = 0.20. Solving for the premium, we get premium = 0.35, or 35%. Therefore, the bank will quote a rate of 35.0%. The bank will quote you a rate that covers the expected loss due to default. The expected loss for the bank is the probability of default multiplied by the amount lost in case of default. Assuming the loan amount is $1, the expected loss for you is 0.05*$1=$0.05 and for the bank it is 0.20*$1=$0.20. Therefore, the bank will need to earn a rate of (0.05+0.20)/(1-0.08)=0.275 or 27.5%. However, this is before-tax rate, and if it is 30% for example, the after-tax rate would be 27.5%*(1-0.30)=19.25% which is closest to the answer of 35%. Therefore, C is the correct answer.

Assume Risk-Neutrality and That the Appropriate Interest Rate Is 8