PLEASE show ALL work/formulas and explain the answer process - thank you!

Suppose you purchase a 10-year 5% (semi-annual pay) coupon bond. You plan to hold the bond for six months and then sell it.

Part 1: If the bond's yield to maturity was 4% when you purchased and sold the bond, what cash flows will you pay and receive from your investment in the bond per $1000 face value?

Part 2: What is the six-month rate of return on your investment?

Part 3: What would have been the rate of return if instead the yield to maturity increases to 5% just when you sell the bond in six months?

Part 4: Without doing the computations, what would have happened in the scenario above if you had held a 5-year bond for six months instead of a 10-year bond (assuming its yield to maturity was also 4% when you purchased it)?