$1.$ Suppose you have just inherited LE$100,000$ and are considering the following options for investing the money to maximize your return:

Option $1$: Hold the money in cash and earn zero return.

Option $2$: Loan the money to one of your friends, at an agreed$-$upon interest rate of $20\%,$ even though you believe there is a $10\%$ chance that this friend would leave town without repaying you.

Option $3$: Invest the money in a corporate bond with a stated return of $18\%,$ although there is a $8\%$ chance the company could go bankrupt.

Option $4$: Put the money in an interest$-$bearing checking account that earns $10\%.$

If you are risk$-$neutral $($that is$,$ neither seek out nor shy away from risk$),$ which of the four options should you choose to maximize your expected return? $($Hint: To calculate the expected return of an outcome, multiply the probability that an event will occur by the outcome of that event.$).$ You must show your calculations. $(10$ points$)$