Please help me answer all the questions shown above with steps. Thanks.

So far, we have assumed that the outcome is all or nothing, that is if an investment succeeds, it will provide the total benefit, and if it fails, nothing is returned. We will now modify the Expected Future Value formula to incorporate a partial success. Recall: FVe = PV(1 + r)"(S) We will consider two possible outcomes with two different payoffs. We can think of a successful investment as providing an interest rater, and an unsuccessful investment as providing an interest rate ry. Consider the following formula: FVg=PV(1 + r.)"(S) + PV (1 + rp)"(1 - 5) Expected Future Value is now a sum of two possible outcomes, with two separate interest rates. 2 Show that the formulation in Part I was a special case of this formula. Hint: You can think of losing your entire investment as an interest rate of negative 100%. If an investment has a 100% chance of successful, what happens to this part of the quation: PV (1 + r)"(1 - S)? Another way of writing this formula is by setting the Future Value of a successful outcome as FVs and the Future Value of a failed outcome as FV. FVs - PV (1 + r.)" FV:= PV (1+r)" Thus, FVg - FVs($) + FV-(1-5) . For a 5 year annual investment, you have a 80% chance of receiving 10% interest rates and a 20% chance of receiving 1% interest rates. If you had decided to invest $1,000 and your investment succeeded, how much money would you have? Now if this investment failed, how much money would you have, assuming you had invested $1,000 as from before? A naive person would say the Expected Future Value is the sum of these two numbers you had calculated. What are they forgetting or not accounting for in their calculation? Calculate the true Expected Future Value of this investment