You want to borrow $20,000 for one year. Your bank believes that there is a 96% probability that you will be able to repay the loan with interest, a 3% probability that you will be able to repay only $15,000, and a 1% probability that you will repay nothing. The risk-free rate is 6%.
-Refer to the information above. If the bank agrees to lend you the money at the risk-free rate of 6%, what will the bank's expected return be?
A)+5.76%
B)+4.01%
C)+5.01%
D)-1.75%

Question

Quizplus · Accepted Answer

The bank's expected return can be calculated by considering the probabilities of the different outcomes and the amounts that would be repaid in each scenario. The expected return is calculated as follows:- With a 96% probability, you repay the loan with 6% interest, so the bank receives $20,000 * 1.06 = $21,200.- With a 3% probability, you repay only $15,000.- With a 1% probability, you repay nothing.The expected value of the repayment is:$$ (0.96 * 21,200) + (0.03 * 15,000) + (0.01 * 0) = 20,352 + 450 + 0 = 20,802 $$The expected return, as a percentage of the $20,000 loan, is:$$ \frac{20,802 - 20,000}{20,000} * 100\% = \frac{802}{20,000} * 100\% = 4.01\% $$Therefore, the bank's expected return is +4.01%.

You Want to Borrow $20,000 for One Year