PLEASE show/explain all work - thank you!

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

(a) If the bonds 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?

(b) What is the six-month rate of return on your investment?

(c) 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? (5 points)

(d) 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)? (5 points)