An investor is considering the purchase of zero coupon U.S. Treasury Bonds. A 30 year zero coupon bond yielding 8 percent can be purchased today for $9.94. At the end of 30 years, the owner of the bond will receive $100. The yield of the bond is related to its price by the following

p= 100/ (1+y)^t

P is the price of the bond, y is the yield, and t is the maturity measured in years.

The investor is planning to purchase a bond today and sell it one year from now. The investor is interested in evaluating the return on the investment in the bond. In addition to the 30 year maturity zero coupon bond, the investor is considering the purchase of zero coupon bonds with maturities of 2,5,10 and 20 years. All of them are currently yielding 8 percent. The investor believes that the yield of each bond one year from now can be modeled by a normal distribution with a mean of 8% and a standard deviation of 1%.

Q1. Using a simulation with 1,000 iterations, estimate the expected return of each bond over the year. Estimate the standard deviation of the returns as well. Use Palliside tools to run the simulation and show the steps.