accounting homework about bond price and yield to maturity

Question:

Suppose Insurance, Inc. would like to buy today a five-year, $1000 bond with a 5% coupon rate and semi-annual coupons. The bond was issued exactly one year earlier today. The current market interest rate on similar bonds is 6%.

What should the price of this bond be today?
Suppose that Insurance, Inc. held the bond until maturity, what should be its total rate of return on this bond?
Now, suppose Insurance, Inc. bought the bond at its fair price today and one year later it sells the bond at $878.34. When Insurance, Inc. sells:
What is the bondâ€™s nominal yield?
What is the bondâ€™s yield to maturity?
What is the bondâ€™s current yield?
What is the companyâ€™s total return on the bond, all else being equal?
If the annual inflation rate were 2%, what is the companyâ€™s real rate of return?
At maturity, what is the price of the bond, assuming the issuer were solvable? Provide a proof for your answer.

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