Your rich uncle asks for your help with a financial deal with his friend. He is considering giving him a loan to help him start a business. Your uncle is considering lending his friend $50,000 and wants earn an expected return similar to his current investments. While your uncle has faith in the project, he assumes there is some chance the project will fail and his friend will not be able to repay him. Together you determine the following scenarios:

i. there is a 5% chance that things will go very wrong and your uncle will get repaid nothing at all

ii. there is a 20% chance that in one year your uncle will only get back $25,000 (with no interest)

iii. there is a 75% chance the venture will be successful and his friend will repay the entire $50,000 plus the stated interest.

You perceive the likelihood of a default occurring as being random (not related to the state of the economy) and your uncle could be earning a 2% annual rate of return on his money for the next year if he left it safely in short term AAA rated bonds. Since this is money that will eventually be passed down to you as his sole heir, your uncle wants your help to determine the annual interest rate he needs to charge his friend on this 1-year loan given the assumed probabilities of default in order to earn, on average, the same return he would receive if he left the money in the AAA bonds. Determine what this interest rate for the loan would have to be.