# Learning Goal: I’m working on a finance question and need an explanation and ans

Learning Goal: I’m working on a finance question and need an explanation and answer to help me learn.1. Suppose that the monthly log return of the stock market index is normally distributed with expected return and volatility of 0.0059 and 0.0662, respectively. If the risk-free rate is 1% (annual, continuously compounded), what is the probability that the stock market index underperforms the risk-free asset over a 10-year investment horizon (percentage point, round to first decimal place)? Matlab can be used.2 . Suppose a 1-year zero-coupon bond trades at price 96.783, and 2-year and 3-year bonds make annual coupon payments at a rate 3% trade at prices 99.789 and 100.285, respectively. (All bonds have a face value of 100.) What is the 3-year pure yield (percentage point, continuously compounded, round to second decimal place)?3. Consider a 10-year bond that makes semiannual coupon payments, which was issued 1 year and 167 days ago. If the coupon rate is 4% and the yield to maturity is 3.07% (continuously compounded), what is the duration (round to second decimal place)?4. Consider a 10-year bond that makes semiannual coupon payments. If the face value is 100, the coupon rate is 2% and the bond price is 84.867, what is the yield to maturity (percentage point, continuously compounded, round to second decimal place)?55. What is the duration of a perpetuity (bond with infinite maturity) with semiannual coupon payments if the yield curve is flat at 4.31% (continuously compounded, round to first decimal place)?Matlab can be used! Please provide solving detail.