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. What return must you promise to pay the bank in order for it to earn the risk-free rate if its assumptions about your ability to repay are accurate?
A)12.76%
B)9.32%
C)10.04%
D)none of the above

Question

Quizplus · Accepted Answer

The bank expects to earn the risk-free rate of 6% on its loan to you, taking into account the probabilities of different repayment outcomes. To find the return you must promise, we calculate the expected repayment and set it equal to the amount that would accrue at the risk-free rate. The expected repayment is calculated as follows: (0.96 * (20,000 + X)) + (0.03 * 15,000) + (0.01 * 0), where X is the interest amount you promise to pay. Solving for X to achieve an expected return equal to the risk-free return on $20,000 does not directly match any of the provided options, indicating that the correct answer is not explicitly listed among the choices.

You Want to Borrow $20,000 for One Year