You need to borrow a loan of $20,000 for one year. Your bank thinks there is a 9

Question

You need to borrow a loan of $20,000 for one year. Your bank thinks there is a 96% probablility that you will repay the loan and the interest, a 3% chance that you will only be able to pay $15,000, and a 1% chance that you won't be able to pay anything back. The risk-free rate is 3%.

With risk neutrality, what interest rate is needed for the bank to earn the risk-free rate, if the assumptions about your repayment abilities are accurate?   

With the same data but with aversion to risk and a risk premium of 3% per annually, which interest rate is needed for the bank to earn 4% annually,  if the assumptions about your repayment abilities are accurate?

Explanation / Answer

Probable amount of Loan to not Recover the amount Amount Prob Amount Loan Amount                   -   96%                -   Loan Amount            5,000 3%             150 Loan Amount          20,000 1%             200 Probable Loss             350 Amount Required By Bank to Earn @ 4% Amount of Loan = 20000 X 4% = $ 800 Total Amount required by Bank = $ 350 + $800 = $ 1150 Rate of Interest to be charged by the bank = 1150/20000 = 5.75%

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