Please solve the following question with step-by-step solutions.

Suppose there are 2 assets, Asset 1 and Asset 2. Both assets have certain payoff

Payoffs	T=1	T=2	T=3
Asset 1	10	10	11
Asset 2	50	50	X

For Parts (1) to (3), Suppose X = 0

(1) When r = 10%, what is the present value of Asset 1 and Asset 2?

(2) What is the set of interest rate r such that the present value of Asset 2 is greater than that of Asset 1?

(3) Suppose r = 20%, find the value of X such that value of the two assets are equal.

(4) What type of asset is Asset 1? Suppose the one period interest rates are ₀₁ =10%, ₁₂ = 20%, ₂₃ = 30%. What is the yield-to-maturity of Asset 1?

(5) Suppose X = 150. Also suppose that the YTM of both Asset 1 and Asset 2 are 30%. Compute the prices at t = 0, t = 1, t = 2 and t = 3 for both assets and plot them. What do you observe from the plot? (Hint: for prices at t = 3, consider the t=3 payoff of Asset 1 as 10+100, and t=3 payoff of Asset 2 as 50+100)