1. One year from today you will deposit $500. How much will you have 3.5 years from today? The continuously compounded annual interest rate is 14%.

2. A company will produce cash flows of either $4 million (with probability = 0.4) or $1 million. r=15%.

a. In expectation, how much will the company produce?

b. What is the company worth today?

3. Your friend agrees to pay you $1,000 if Biden wins re-election exactly 4 years from today. You agree to pay $2,500 if he does not win. r=20%. Assume that the bet is fair, and neither of you requires payment today to incentivize you to make the bet. What must be the probability that Biden wins re-election?

4. Your friend agrees to pay you $1,000 if the S&P500 Index is above $4,000 exactly one year from today. Today, you pay $350 for the right to enter the bet. r=8%. The Index will end up above $4,000 with probability = 0.7. For this to be a fair bet, how much must you agree to pay if the Index is below $4,000?

5. Your utility function is u(w) = w². You will receive either $4 or $1 with equal probability.

a. how much will you receive in expectation?

b. in expectation, what is your utility?

c. how much worse off would you be if you removed all risk and received your expected wealth with certainty?

For questions 5-9, assume the underlying asset is a stock worth $55 today. Also assume the following spot prices will be realized in the future S₁=$62 and S₂=47. Also assume that C(50,1)=$7 and P(50,2)=$3. r=15%.

5.

a. What is the payoff of a long forward with F₁=$60?

b. What is the profit of a long forward with F₁=$60?

6.

a. What is the payoff of a short forward with F₂=$70?

b. What is the profit of a short forward with F₂=$70?

7.

a. What is the payoff of a short one-year call option with strike=50?

b. What is the profit of a short one-year call option with strike=50?

8.

a. What is the payoff of a long two-year put option with strike=50?

b. What is the profit of a short two-year put option with strike=50?

9.

a. If you formed a long position in the underlying asset at t=0 and exited the position at t=2, what is your profit?

b. If you formed a short position in the underlying asset at t=0 and exited the position at t=1, what is your profit?