Using excel You are considering buying a risky bond. The bond has a $$1,000$ face value, a $1-$year maturity, and a coupon rate of $6\%.$ Coupon payments are made annually. You believe the probability the company will survive to pay off the bond is $78\%.$ You also believe there is a $22\%$ probability the company will default within the first $2$ months, in which case you will be able to recover $25\%$ of the bond's face value at the end of year $1.$ The bond is selling for $$820.$

a$.$ Calculate the expected return on this bond on an annual basis.

b$.$ Use Goal Seek or Solver to determine the probability of survival that would yield an expected annual return of $10\%.$

Use excel and show the formulas used in each cell